[Numerical Modeling 15] Finite difference solution of the diffusion equation

In this video, we want to go a bit deeper into the details of the finite difference method. And what can be better for it than the diffusion equation, with which we deal a lot in the Tux Riders projects? Let’s use all the things we have learned so far plus a few new things to numerically solve the heat transfer equation (as an example of the diffusion equation) in 1-D and 2-D.

Educational Materials:

Topics covered:
🎯 Introduction to the diffusion equation
🎯 The difference between an implicit and an explicit formulation in numerical computing
🎯 Benefits and limitations of implicit and explicit finite difference solution of diffusion equation
🎯 Concepts and implementation of commonly-used boundary conditions, Dirichlet and Neumann
🎯 Solving 1-D and 2-D diffusion equations using implicit and explicit finite difference

Chapters in this video!
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00:00 - Intro
02:53 - Explicit finite difference solution of a 1D diffusion equation
05:31 - Dirichlet and Neumann boundary conditions
09:36 - Implicit finite difference formulation for a 1D diffusion equation
13:50 - Implementation of implicit finite difference
17:47 - Implicit formulation is unconditionally stable!
20:48 - Explicit finite difference for 2D diffusion equation
25:54 - Implicit finite difference for 2D diffusion equation

[ipepperify]

This was awesome, everything I needed to know. Thank you!