# Category: Finite differences

Hermite interpolation
In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation. Lagrange interpolation allows computing a
Geodesic grid
A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron.
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
Table of Newtonian series
In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence written in the form where is the binomial coefficient and is the falling factorial. Newtonian series often appear
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
Delta operator
In mathematics, a delta operator is a shift-equivariant linear operator on the vector space of polynomials in a variable over a field that reduces degrees by one. To say that is shift-equivariant mean
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
Carlson's theorem
In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it states that two different analytic functions whic
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
Mean value theorem (divided differences)
In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives.
Umbral calculus
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them.
Newton polynomial
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is som
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
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
Nørlund–Rice integral
In mathematics, the Nørlund–Rice integral, sometimes called Rice's method, relates the nth forward difference of a function to a line integral on the complex plane. It commonly appears in the theory o
Thiele's interpolation formula
In mathematics, Thiele's interpolation formula is a formula that defines a rational function from a finite set of inputs and their function values . The problem of generating a function whose graph pa
De numeris triangularibus et inde de progressionibus arithmeticis: Magisteria magna
De numeris triangularibus et inde de progressionibus arithmeticis: Magisteria magna is a 38-page mathematical treatise written in the early 17th century by Thomas Harriot, lost for many years, and fin
Falling and rising factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial The rising factorial (sometimes called th
Indefinite sum
In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by or , is the linear operator, inverse of the forward difference operator . It relates to the for
Divided differences
In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's difference engine, an early mechanical calculat
Bernoulli umbra
In Umbral calculus, Bernoulli umbra is an , a formal symbol, defined by the relation , where is the index-lowering operator, also known as evaluation operator and are Bernoulli numbers, called moments
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.
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
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
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
Faulhaber's formula
In mathematics, Faulhaber's formula, named after the early 17th century mathematician Johann Faulhaber, expresses the sum of the p-th powers of the first n positive integers as a (p + 1)th-degree poly
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
Reciprocal difference
In mathematics, the reciprocal difference of a finite sequence of numbers on a function is defined inductively by the following formulas:
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
Difference polynomials
In mathematics, in the area of complex analysis, the general difference polynomials are a polynomial sequence, a certain subclass of the Sheffer polynomials, which include the Newton polynomials, Selb