Numerically Solving Partial Differential Equations

In this video we show how to numerically solve partial differential equations by numerically approximating partial derivatives using the finite difference method. We develop an algorithm that will allow direct numerical simulation of a partial differential equation.

Topics and Timestamps:
0:00 – Introduction
1:04 – Fokker-Planck equation
7:45 – Verifying and visualizing the analytical solution in Mathematica
15:29 – The Finite Difference Method
57:57 – Converting a continuous PDE into an algebraic equation
1:07:57 – Boundary conditions
1:14:29 – Math Joke: Star Wars error
1:15:53 – Implementation of numerical solution in Matlab

A sample Mathematica notebook that accompanies this lecture is located at
http://faculty.washington.edu/lum/EducationalVideoFiles/PDEs13/NumericalPDEs.nb.

A sample Matlab script that accompanies this lecture is located at http://faculty.washington.edu/lum/EducationalVideoFiles/PDEs13/NumericalPDEs.m.

Additional videos in this series:
-Introduction to Partial Differential Equations (https://youtu.be/THjaxvPBGOU)
-Standing Waves Demonstration (https://youtu.be/42WBuhVJ7sA)
-Derivation of the 1D Wave Equation (https://youtu.be/IAut5Y-Ns7g)
-Solving the 1D Wave Equation (https://youtu.be/lMRnTd8yLeY)
-Heat Transfer Demonstration (https://youtu.be/FsLFZT44l48)
-Derivation of the Heat Equation (https://youtu.be/ixsRJPlO_rc)
-Solving the 1D Heat Equation (https://youtu.be/I3jiMhVGmcg)
-Derivation and Solution of Laplace’s Equation (https://youtu.be/GCESkCyZt4g)
-Derivation of the 2D Wave Equation (https://youtu.be/KAS7JBztw8E)
-Solving the 2D Wave Equation (https://youtu.be/Whp6jolTu34)
-Numerically Solving Partial Differential Equations (https://youtu.be/ZSNl5crAvsw)

Associated videos on software tools relevant to PDEs include:
-Creating Movies and Animations in Mathematica (https://youtu.be/S03e6dwM100)
-Creating Movies and Animations in Matlab (https://youtu.be/3I1_5M7Okqo)

You can see all the videos related to partial differential equations at
https://www.youtube.com/playlist?list=PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx

#PDEs

Видео Numerically Solving Partial Differential Equations канала Christopher Lum