- Applied mathematics
- >
- Algorithms
- >
- Numerical analysis
- >
- Numerical differential equations

- Applied mathematics
- >
- Computational mathematics
- >
- Numerical analysis
- >
- Numerical differential equations

- Calculus
- >
- Differential calculus
- >
- Differential equations
- >
- Numerical differential equations

- Equivalence (mathematics)
- >
- Approximations
- >
- Numerical analysis
- >
- Numerical differential equations

- Fields of mathematics
- >
- Computational mathematics
- >
- Numerical analysis
- >
- Numerical differential equations

- Mathematical analysis
- >
- Fields of mathematical analysis
- >
- Numerical analysis
- >
- Numerical differential equations

- Mathematical logic
- >
- Algorithms
- >
- Numerical analysis
- >
- Numerical differential equations

- Mathematical relations
- >
- Approximations
- >
- Numerical analysis
- >
- Numerical differential equations

- Rates
- >
- Differential calculus
- >
- Differential equations
- >
- Numerical differential equations

- Subtraction
- >
- Differential calculus
- >
- Differential equations
- >
- Numerical differential equations

- Theoretical computer science
- >
- Algorithms
- >
- Numerical analysis
- >
- Numerical differential equations

- Theoretical computer science
- >
- Mathematics of computing
- >
- Numerical analysis
- >
- Numerical differential equations

Flux limiter

Flux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations (PDEs)

Weakened weak form

Weakened weak form (or W2 form) is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings. These numerical methods are applicable to solid

Milstein method

In mathematics, the Milstein method is a technique for the approximate numerical solution of a stochastic differential equation. It is named after who first published it in 1974.

Leimkuhler–Matthews method

The Leimkuhler-Matthews method (or LM method in its original paper ) is an algorithm for finding discretized solutions to the Brownian dynamics where is a constant and can be thought of as a potential

Cash–Karp method

In numerical analysis, the Cash–Karp method is a method for solving ordinary differential equations (ODEs). It was proposed by Professor Jeff R. Cash from Imperial College London and Alan H. Karp from

Raviart–Thomas basis functions

In applied mathematics, Raviart–Thomas basis functions are vector basis functions used in finite element and boundary element methods. They are regularly used as basis functions when working in electr

Finite difference methods for option pricing

Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo

Spectral element method

In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewi

AUSM

AUSM stands for Advection Upstream Splitting Method. It is developed as a numerical inviscid flux function for solving a general system of conservation equations. It is based on the upwind concept and

High-resolution scheme

High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following prope

Numerov's method

Numerov's method (also called Cowell's method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is a fourth-order linear

Variational integrator

Variational integrators are numerical integrators for Hamiltonian systems derived from the Euler–Lagrange equations of a discretized Hamilton's principle. Variational integrators are momentum-preservi

Runge–Kutta method (SDE)

In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation. It is a generalisation of the Runge–Kutta meth

Total variation diminishing

In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this me

Finite-difference time-domain method

Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational e

MUSCL scheme

In the study of partial differential equations, the MUSCL scheme is a finite volume method that can provide highly accurate numerical solutions for a given system, even in cases where the solutions ex

Leapfrog integration

In numerical analysis, leapfrog integration is a method for numerically integrating differential equations of the form or equivalently of the formparticularly in the case of a dynamical system of clas

Moving particle semi-implicit method

The moving particle semi-implicit (MPS) method is a computational method for the simulation of incompressible free surface flows. It is a macroscopic, deterministic particle method (Lagrangian mesh-fr

Alternating-direction implicit method

In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equati

Upwind scheme

In computational physics, the term upwind scheme (sometimes advection scheme) typically refers to a class of numerical discretization methods for solving hyperbolic partial differential equations, in

Composite methods for structural dynamics

Composite methods are an approach applied in structural dynamics and related fields. They combine various methods in each time step, in order to acquire the advantages of different methods. The existi

Energy drift

In computer simulations of mechanical systems, energy drift is the gradual change in the total energy of a closed system over time. According to the laws of mechanics, the energy should be a constant

Microscale and macroscale models

Microscale models form a broad class of computational models that simulate fine-scale details, in contrast with macroscale models, which amalgamate details into select categories. Microscale and macro

Mesh generation

Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells.Often these cells form a simplicial complex.Usually the

Céa's lemma

Céa's lemma is a lemma in mathematics. Introduced by Jean Céa in his Ph.D. dissertation, it is an important tool for proving error estimates for the finite element method applied to elliptic partial d

Fast marching method

The fast marching method is a numerical method created by James Sethian for solving boundary value problems of the Eikonal equation: Typically, such a problem describes the evolution of a closed surfa

Meshfree methods

In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with

Stencil (numerical analysis)

In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate

Uniform theory of diffraction

In numerical analysis, the uniform theory of diffraction (UTD) is a high-frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in

Discrete Laplace operator

In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph

Method of moments (electromagnetics)

The method of moments (MoM), also known as the moment method and method of weighted residuals, is a numerical method in computational electromagnetics. It is used in computer programs that simulate th

Runge–Kutta–Fehlberg method

In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German

Central differencing scheme

In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and pro

Verlet integration

Verlet integration (French pronunciation: [vɛʁˈlɛ]) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dyn

Bi-directional delay line

In mathematics, a bi-directional delay line is a numerical analysis technique used in computer simulation for solving ordinary differential equations by converting them to hyperbolic equations. In thi

Numerical dispersion

In computational mathematics, numerical dispersion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher dispersivity than the true medi

Vorticity confinement

Vorticity confinement (VC), a physics-based computational fluid dynamics model analogous to shock capturing methods, was invented by Dr. John Steinhoff, professor at the University of Tennessee Space

Symplectic integrator

In mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are cano

WENO methods

In numerical solution of differential equations, WENO (weighted essentially non-oscillatory) methods are classes of high-resolution schemes. WENO are used in the numerical solution of hyperbolic parti

Partial element equivalent circuit

Partial element equivalent circuit method (PEEC) is partial inductance calculation used for interconnect problems from early 1970s which is used for numerical modeling of electromagnetic (EM) properti

Midpoint method

In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation, The explicit midpoint method is given by the formula

Infinite element method

The infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The method divides the domain concerned i

Multisymplectic integrator

In mathematics, a multisymplectic integrator is a numerical method for the solution of a certain class of partial differential equations, that are said to be multisymplectic. Multisymplectic integrato

Immersed boundary method

In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coup

Weak formulation

Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential e

Characteristic mode analysis

Characteristic modes (CM) form a set of functions which, under specific boundary conditions, diagonalizes operator relating field and induced sources. Under certain conditions, the set of the CM is un

Geometric integrator

In the mathematical field of numerical ordinary differential equations, a geometric integrator is a numerical method that preserves geometric properties of the exact flow of a differential equation.

Lax–Wendroff method

The Lax–Wendroff method, named after Peter Lax and Burton Wendroff, is a numerical method for the solution of hyperbolic partial differential equations, based on finite differences. It is second-order

Extended discrete element method

The extended discrete element method (XDEM) is a numerical technique that extends the dynamics of granular material or particles as described through the classical discrete element method (DEM) (Cunda

Eigenvalues and eigenvectors of the second derivative

Explicit formulas for eigenvalues and eigenvectors of the second derivative with different boundary conditions are provided both for the continuous and discrete cases. In the discrete case, the standa

General linear methods

General linear methods (GLMs) are a large class of numerical methods used to obtain numerical solutions to ordinary differential equations. They include multistage Runge–Kutta methods that use interme

Backward Euler method

In numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary differential equations. It

Momentum (electromagnetic simulator)

Momentum is 3-D planar EM simulation software for electronics and antenna analysis, a partial differential equation solver of Maxwell's equations based on the method of moments. It is a 3-D planar ele

Exponential integrator

Exponential integrators are a class of numerical methods for the solution of ordinary differential equations, specifically initial value problems. This large class of methods from numerical analysis i

Perfectly matched layer

A perfectly matched layer (PML) is an artificial absorbing layer for wave equations, commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, esp

Numerical resistivity

Numerical resistivity is a problem in computer simulations of ideal magnetohydrodynamics (MHD). It is a form of numerical diffusion. In near-ideal MHD systems, the magnetic field can diffuse only very

Semi-implicit Euler method

In mathematics, the semi-implicit Euler method, also called symplectic Euler, semi-explicit Euler, Euler–Cromer, and Newton–Størmer–Verlet (NSV), is a modification of the Euler method for solving Hami

Adaptive step size

In mathematics and numerical analysis, an adaptive step size is used in some methods for the numerical solution of ordinary differential equations (including the special case of numerical integration)

Compact stencil

In mathematics, especially in the areas of numerical analysis called numerical partial differential equations, a compact stencil is a type of stencil that uses only nine nodes for its discretization m

List of Runge–Kutta methods

Runge–Kutta methods are methods for the numerical solution of the ordinary differential equation Explicit Runge–Kutta methods take the form Stages for implicit methods of s stages take the more genera

Euler–Maruyama method

In Itô calculus, the Euler–Maruyama method (also called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is an extension of the Eule

ENO methods

ENO (essentially non-oscillatory) methods are classes of high-resolution schemes in numerical solution of differential equations.

Principles of grid generation

No description available.

Lax–Wendroff theorem

In computational mathematics, the Lax–Wendroff theorem, named after Peter Lax and Burton Wendroff, states that if a conservative numerical scheme for a hyperbolic system of conservation laws converges

Method of fundamental solutions

In scientific computation and simulation, the method of fundamental solutions (MFS) is a technique for solving partial differential equations based on using the fundamental solution as a basis functio

Explicit and implicit methods

Explicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is req

Dynamic design analysis method

The dynamic design analysis method (DDAM) is a US Navy-developed analytical procedure for evaluating the design of equipment subject to dynamic loading caused by underwater explosions (UNDEX). The ana

Five-point stencil

In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors". It is us

Fast sweeping method

In applied mathematics, the fast sweeping method is a numerical method for solving boundary value problems of the Eikonal equation. where is an open set in , is a function with positive values, is a w

Spectral method

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differenti

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the tradi

Split-step method

In numerical analysis, the split-step (Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation. The name ar

Rayleigh–Ritz method

The Rayleigh–Ritz method is a direct numerical method of approximating eigenvalues, originated in the context of solving physical boundary value problems and named after Lord Rayleigh and Walther Ritz

Finite difference method

In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial dom

Linear multistep method

Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in ti

Volume of fluid method

In computational fluid dynamics, the volume of fluid (VOF) method is a free-surface modelling technique, i.e. a numerical technique for tracking and locating the free surface (or fluid–fluid interface

Strang splitting

Strang splitting is a numerical method for solving differential equations that are decomposable into a sum of differential operators. It is named after Gilbert Strang. It is used to speed up calculati

Runge–Kutta methods

In numerical analysis, the Runge–Kutta methods (English: /ˈrʊŋəˈkʊtɑː/ RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discr

Higher-order compact finite difference scheme

High-order compact finite difference schemes are used for solving third-order differential equations created during the study of obstacle boundary value problems. They have been shown to be highly acc

Shooting method

In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem. It involves finding solutions to the initial value problem for d

Particle-in-cell

In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in

Singular boundary method

In numerical analysis, the singular boundary method (SBM) belongs to a family of meshless boundary collocation techniques which include the method of fundamental solutions (MFS), boundary knot method

Euler method

In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initi

Material point method

The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization me

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerica

Diffuse element method

In numerical analysis the diffuse element method (DEM) or simply diffuse approximation is a meshfree method. The diffuse element method was developed by B. Nayroles, G. Touzot and Pierre Villon at the

Finite difference

A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by fini

Courant–Friedrichs–Lewy condition

In mathematics, the convergence condition by Courant–Friedrichs–Lewy is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically

Non-compact stencil

In numerical mathematics, a non-compact stencil is a type of discretization method, where any node surrounding the node of interest may be used in the calculation. Its computational time grows with an

Numerical diffusion

Numerical diffusion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher diffusivity than the true medium. This phenomenon can be parti

Discrete Poisson equation

In mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation. In it, the discrete Laplace operator takes the place of the Laplace operator. The discrete Poisso

Finite element method in structural mechanics

The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems

Zero stability

Zero-stability, also known as D-stability in honor of Germund Dahlquist, refers to the stability of a numerical scheme applied to the simple initial value problem . A linear multistep method is zero-s

Modal analysis using FEM

The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. It is common to use the finite element metho

Adaptive mesh refinement

In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time th

MacCormack method

In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite differen

Analytic element method

The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota. It is simil

Multiphase particle-in-cell method

The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC met

Stiff equation

In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.

Direct stiffness method

As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures inclu

Constraint (computational chemistry)

In computational chemistry, a constraint algorithm is a method for satisfying the Newtonian motion of a rigid body which consists of mass points. A restraint algorithm is used to ensure that the dista

Godunov's theorem

In numerical analysis and computational fluid dynamics, Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the theory of high

Lax–Friedrichs method

The Lax–Friedrichs method, named after Peter Lax and Kurt O. Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can

Cyclic reduction

Cyclic reduction is a numerical method for solving large linear systems by repeatedly splitting the problem. Each step eliminates even or odd rows and columns of a matrix and remains in a similar form

Cell lists

Cell lists (also sometimes referred to as cell linked-lists) is a data structure in molecular dynamics simulations to find all atom pairs within a given cut-off distance of each other. These pairs are

Godunov's scheme

In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by S. K. Godunov in 1959, for solving partial differential equations. One can thi

Discrete calculus

Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalization

Natural element method

The natural element method (NEM) is a meshless method to solve partial differential equation, where the elements do not have a predefined shape as in the finite element method, but depend on the geome

Backward differentiation formula

The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations. They are linear multistep methods that, for a given functio

Boundary knot method

In numerical mathematics, the boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent decades have witnessed a research boom on the

Infinite difference method

In mathematics, infinite difference methods are numerical methods for solving differential equations by approximating them with difference equations, in which infinite differences approximate the deri

Multilevel fast multipole method

The multilevel fast multipole method (MLFMM) is used along with method of moments (MoM) a numerical computational method of solving linear partial differential equations which have been formulated as

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods

Walk-on-spheres method

In mathematics, the walk-on-spheres method (WoS) is a numerical probabilistic algorithm, or Monte-Carlo method, used mainly in order to approximate the solutions of some specific boundary value proble

History of numerical solution of differential equations using computers

Differential equations, in particular Euler equations, rose in prominence during World War II in calculating the accurate trajectory of ballistics, both rocket-propelled and gun or cannon type project

Extended finite element method

The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite eleme

Parareal

Parareal is a parallel algorithm from numerical analysis and used for the solution of initial value problems.It was introduced in 2001 by Lions, Maday and Turinici. Since then, it has become one of th

Mimesis (mathematics)

In mathematics, mimesis is the quality of a numerical method which imitates some properties of the continuum problem. The goal of numerical analysis is to approximate the continuum, so instead of solv

Heun's method

In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is

Beeman's algorithm

Beeman's algorithm is a method for numerically integrating ordinary differential equations of order 2, more specifically Newton's equations of motion . It was designed to allow high numbers of particl

Smoothed finite element method

Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed by combining meshfree methods with the fini

Direct multiple shooting method

In the area of mathematics known as numerical ordinary differential equations, the direct multiple shooting method is a numerical method for the solution of boundary value problems. The method divides

Boundary element method

The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form)

Shock-capturing method

In computational fluid dynamics, shock-capturing methods are a class of techniques for computing inviscid flows with shock waves. The computation of flow containing shock waves is an extremely difficu

Beam and Warming scheme

In numerical mathematics, Beam and Warming scheme or Beam–Warming implicit scheme introduced in 1978 by Richard M. Beam and R. F. Warming, is a second order accurate implicit scheme, mainly used for s

Dormand–Prince method

In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations. The method is a member of the Runge–Kutta family of ODE solv

Galerkin method

In mathematics, in the area of numerical analysis, Galerkin methods, named after the Russian mathematician Boris Galerkin, convert a continuous operator problem, such as a differential equation, commo

Finite-difference frequency-domain method

The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics, based on finite-difference approximations of th

Discontinuous Galerkin method

In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite vol

Method of lines

The method of lines (MOL, NMOL, NUMOL) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. By reducing a PDE to a single continuous dimensio

Roe solver

The Roe approximate Riemann solver, devised by Phil Roe, is an approximate Riemann solver based on the Godunov scheme and involves finding an estimate for the intercell numerical flux or Godunov flux

Discrete element method

A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is

Pantelides algorithm

Pantelides algorithm in mathematics is a systematic method for reducing high-index systems of differential-algebraic equations to lower index. This is accomplished by selectively adding differentiated

Loubignac iteration

In applied mathematics, Loubignac iteration is an iterative method in finite element methods. It gives continuous stress field. It is named after Gilles Loubignac, who published the method in 1977.

Finite volume method

The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.In the finite volume method, volume integrals in a partial

Particle method

In the field of numerical analysis, particle methods discretize fluid into particles. Particle methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computi

Gradient discretisation method

In numerical mathematics, the gradient discretisation method (GDM) is a framework which contains classical and recent numerical schemes for diffusion problems of various kinds: linear or non-linear, s

Finite pointset method

In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows. In this approach (of

Laplacian matrix

In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Name

Upwind differencing scheme for convection

The upwind differencing scheme is a method used in numerical methods in computational fluid dynamics for convection–diffusion problems. This scheme is specific for Peclet number greater than 2 or less

Kronecker sum of discrete Laplacians

In mathematics, the Kronecker sum of discrete Laplacians, named after Leopold Kronecker, is a discrete version of the separation of variables for the continuous Laplacian in a rectangular cuboid domai

Crank–Nicolson method

In numerical analysis, the Crank–Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in

Numerical methods for differential equations

Numerical methods for differential equations may refer to:
* Numerical methods for ordinary differential equations, methods used to find numerical approximations to the solutions of ordinary differen

Boundary particle method

In applied mathematics, the boundary particle method (BPM) is a boundary-only meshless (meshfree) collocation technique, in the sense that none of inner nodes are required in the numerical solution of

Fast multipole method

The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem. It does this by expanding the system Green's functi

False diffusion

False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more accurate central difference scheme can be used

FTCS scheme

In numerical analysis, the FTCS (Forward Time Centered Space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations.

Stochastic Eulerian Lagrangian method

In computational fluid dynamics, the Stochastic Eulerian Lagrangian Method (SELM) is an approach to capture essential features of fluid-structure interactions subject to thermal fluctuations while int

Newmark-beta method

The Newmark-beta method is a method of numerical integration used to solve certain differential equations. It is widely used in numerical evaluation of the dynamic response of structures and solids su

Finite difference coefficient

In mathematics, to approximate a derivative to an arbitrary order of accuracy, it is possible to use the finite difference. A finite difference can be central, forward or backward.

Interval boundary element method

Interval boundary element method is classical boundary element method with the interval parameters.Boundary element method is based on the following integral equation The exact interval solution on th

Smoothed-particle hydrodynamics

Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan

Collocation method

In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-di

Virtual Cell

Virtual Cell (VCell) is an open-source software platform for modeling and simulation of living organisms, primarily cells. It has been designed to be a tool for a wide range of scientists, from experi

Regularized meshless method

In numerical mathematics, the regularized meshless method (RMM), also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method designed to sol

Lax equivalence theorem

In numerical analysis, the Lax equivalence theorem is a fundamental theorem in the analysis of finite difference methods for the numerical solution of partial differential equations. It states that fo

Proper orthogonal decomposition

The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational fluid dynamics and structural analysis (lik

Coupled mode theory

Coupled mode theory (CMT) is a perturbational approach for analyzing the coupling of vibrational systems (mechanical, optical, electrical, etc.) in space or in time. Coupled mode theory allows a wide

Stretched grid method

The stretched grid method (SGM) is a numerical technique for finding approximate solutions of various mathematical and engineering problems that can be related to an elastic grid behavior.In particula

Trefftz method

In mathematics, the Trefftz method is a method for the numerical solution of partial differential equations named after the German mathematician (de) (1888–1937). It falls within the class of finite e

L-stability

Within mathematics regarding differential equations, L-stability is a special case of A-stability, a property of Runge–Kutta methods for solving ordinary differential equations.A method is L-stable if

P-FEM

p-FEM or the p-version of the finite element method is a numerical method for solving partial differential equations. It is a discretization strategy in which the finite element mesh is fixed and the

Quantized state systems method

The quantized state systems (QSS) methods are a family of numerical integration solvers based on the idea of state quantization, dual to the traditional idea of time discretization.Unlike traditional

© 2023 Useful Links.