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/tgautam03/0Mean1Sigma/tree/master/WaveSim References: - FDM 5-point stencil: https://math.stackexchange.com/questions/262701/how-to-obtain-prove-5-stencil-formula-for-2nd-derivative - Excellent resources on Von Neumann analysis: - MIT notes:(https://math.mit.edu/classes/18.300/Notes/Notes_vNSA.pdf) - Jeff Chasnov's YouTube video: (https://www.youtube.com/watch?v=QUiUGNwNNmo) - LMU Seismology: (https://www.youtube.com/watch?v=5_VtrWGaEGM) - Absorbing boundary condition:(https://www.jpier.org/ac_api/download.php?id=0506213) Video clips credits: - https://www.youtube.com/watch?v=rSKMYc1CQHE - https://www.youtube.com/watch?v=XmzBREkK8kY&t=4s - https://www.youtube.com/watch?v=9IULfQH7E90&t=33s - https://www.youtube.com/watch?v=NorXFOobehY&t=403s - https://www.youtube.com/watch?v=cM47L5RddsM - https://www.youtube.com/watch?v=TvlIfSlLB0c - https://www.youtube.com/watch?v=aMhscBkcmQI 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