Wave Simulation from scratch using finite difference method

CORRECTION at 6:16, the equation should end with dt^2 * s(x,t).
CORRECTION at 3:48, the delta function approximation should be d(x-a)=1/dx when x is greater than a-dx and x is less than a+dx, and 0 elsewhere

WaveSim code repository: https://github.com/tgautam03/WaveSim

Animations were generated using Manim, and the code can be found here: https://github.com/tgautam03/0Mean1Si...

References:
- FDM 5-point stencil: https://math.stackexchange.com/questi...
- Excellent resources on Von Neumann analysis:
- MIT notes:(https://math.mit.edu/classes/18.300/N...)
- Jeff Chasnov's YouTube video: (   • Von Neumann Stability Analysis of the...  )
- LMU Seismology: (   • Von Neumann analysis: derivation of t...  )
- Absorbing boundary condition:(https://www.jpier.org/ac_api/download...)

Video clips credits:
-    • Coding Adventure: Simulating Fluids  
-    • 18 - How to write a FLIP water / flui...  
-    • Writing a Physics Engine from scratch...  
-    • Teaching myself C so I can build a pa...  
-    • MATLAB 2D Fluid Simulation  
-    • Heat Transfer Simulation  
-    • Animated model of P & S wave propagat...  

00:00 - Opening
00:34 - Wave equations
00:53 - 1D Wave Equation
04:22 - Taylor Series
05:56 - Finite Differences
08:12 - 1D wave simulation demo
10:56 - Von Neumann Analysis
12:03 - Different boundary conditions
12:41 - Absorbing Boundary Condition
13:20 - 2D Wave Equation
14:31 - 2D wave simulation demo
16:22 - Final thoughts