[Numerical Modeling 13] Finite difference method for solving partial differential equations (PDEs)

After learning how to use numerical techniques for ordinary differential equations, it’s time to dive into partial differential equations (PDEs), the kind of equations we, the Tux Riders (and of course so many modelers around the globe also), use a lot to model a wide range of different phenomena in science and engineering. Let’s see how we can employ this powerful method to solve complicated PDEs, but with easy steps first.

Educational Materials:

Topics covered:
🎯 Discretizing space and time
🎯 How does numerical differentiation work in action?
🎯 Concepts of numerical computing for solving a 1D convection equation
🎯 The concept of truncation error in numerical methods
🎯 Dealing with nonlinear PDEs

Chapters in this video!
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00:00 – Intro
01:20 - Discretizing time and space for partial differential equations
05:48 - Concept of various forms of numerical differentiation
09:45 - Numerical solution of 1D linear convection PDE
13:09 - Solving a sample problem for convection equation
15:58 - Big O notation and truncation error
17:28 - Dealing with non-linear convection equation

[deboy]

I am working calmly through the playlists. They are amazingly clear and help me a lot for understanding the theory.

[AangContreras]

I have just discovered your channel and is gold! Keep up the good work n.n

[djdelta]

What is the most challenging PDE you have solved and what implementation did you have to do to make it work or more robust?