Finite differences | Numerical differential equations
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 domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis.Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element methods. (Wikipedia).
Finite Difference Method for finding roots of functions including an example and visual representation. Also includes discussions of Forward, Backward, and Central Finite Difference as well as overview of higher order versions of Finite Difference. Chapters 0:00 Intro 0:04 Secant Method R
From playlist Root Finding
From playlist ℕumber Theory
Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations
Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3
From playlist Solving Systems of Nonlinear Equations
Follow-Up: Finite Difference Method
Original Video here: https://youtu.be/scQ51q_1nhw Videos mentioned: James Tanton https://youtu.be/_5vU48kf7NY Mathologer https://youtu.be/4AuV93LOPcE More on Gilbreath's conjecture here: https://primes.utm.edu/glossary/page.php?sort=GilbreathsConjecture Here is finite differences on wik
From playlist My Maths Videos
Method of Finite Differences - Formula for First n Squares
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
From playlist Proofs
Central Difference Approximation | Lecture 61 | Numerical Methods for Engineers
How to approximate the first and second derivatives by a central difference formula. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.yo
From playlist Numerical Methods for Engineers
Further Pure 2 FP2 Method of Differences 4 Summing Series Tough Example
www.m4ths.com GCSE and A Level Worksheets, videos and helpbooks. Full course help for Foundation and Higher GCSE 9-1 Maths All content created by Steve Blades
From playlist Further Pure 2 FP2 Method of Differences
Further Pure 2 FP2 Method of Differences 8 Summing Series
www.m4ths.com GCSE and A Level Worksheets, videos and helpbooks. Full course help for Foundation and Higher GCSE 9-1 Maths All content created by Steve Blades
From playlist Further Pure 2 FP2 Method of Differences
Lecture: Higher-order Accuracy Schemes for Differentiation and Integration
The accuracy of the differentiation approximations is considered and new schemes are developed to lower the error. Integration is also introduced as a numerical algorithm.
From playlist Beginning Scientific Computing
Ari Stern: Hybrid finite element methods preserving local symmetries and conservation laws
Abstract: Many PDEs arising in physical systems have symmetries and conservation laws that are local in space. However, classical finite element methods are described in terms of spaces of global functions, so it is difficult even to make sense of such local properties. In this talk, I wil
From playlist Numerical Analysis and Scientific Computing
Lecture 24 (CEM) -- Introduction to Variational Methods
This lecture introduces to the student to variational methods including finite element method, method of moments, boundary element method, and spectral domain method. It describes the Galerkin method for transforming a linear equation into matrix form as well as populating the global matr
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
Numerical Homogenization by Localized Orthogonal Decomposition (Lecture 3) by Daniel Peterseim
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Convergent Evolving Surface Finite Element Algorithms for Geometric Evolution Equations
Professor Christian Lubich University of Tübingen, Germany
From playlist Distinguished Visitors Lecture Series
Mod-01 Lec-23 Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Lecture 16 (CEM) -- Beam Propagation Method
This lecture steps the student through the formulation and implementation of a basic finite-difference beam propagation method. A brief overview of wide-angle and bi-directional BPM is given, but not discussed in detail. Prerequisite Lectures: 10
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
Numerical Homogenization by Localized Orthogonal Decomposition (Lecture 1) by Daniel Peterseim
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Twitch Talks - Nonlinear Finite Elements
Presenter: Oliver Ruebenkoeig Wolfram Research developers demonstrate the new features of Version 12 of the Wolfram Language that they were responsible for creating. Previously broadcast live on July 25, 2019 at twitch.tv/wolfram. For more information, visit: https://www.wolfram.com/langu
From playlist Twitch Talks
Further Pure 2 FP2 Method of Differences 1 Summing Series
www.m4ths.com GCSE and A Level Worksheets, videos and helpbooks. Full course help for Foundation and Higher GCSE 9-1 Maths All content created by Steve Blades
From playlist Further Pure 2 FP2 Method of Differences
Numerical Hydrodynamics: Part 3 by Ian Hawke
PROGRAM: GRAVITATIONAL WAVE ASTROPHYSICS (ONLINE) ORGANIZERS : Parameswaran Ajith, K. G. Arun, Sukanta Bose, Bala R. Iyer, Resmi Lekshmi and B Sathyaprakash DATE: 18 May 2020 to 22 May 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been cancelled. Howe
From playlist Gravitational Wave Astrophysics (Online) 2020