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Why Runge-Kutta is SO Much Better Than Euler's Method #somepi

Phanimations 173,946 7 months ago
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Did some stuff with Euler's Method and Runge-Kutta that I thought I'd share. #somepi Link to interactive Web.VPython simulation: https://trinket.io/library/trinkets/1fe7d9cdd6 Link to code for the video: https://github.com/shawnseanspencer/manimations/blob/main/Runge_Kutta.py Timestamps: 0:00 Intro 1:29 Harmonic Oscillator 2:34 Euler's Method 5:03 Implicit Euler's Method 8:15 RK2 10:03 RK4 11:57 Outro & Bonus Music Ravel: Gaspard de la Nuit - Ondine (Performer: Bernd Kreuger) https://commons.wikimedia.org/wiki/File:Maurice_Ravel_Ondine.ogg “Impact Prelude” - Kevin Macleod https://www.youtube.com/watch?v=on7qf4jUbgw “Late Night Radio” - Kevin Macleod https://www.youtube.com/watch?v=QhtL-6Cf5Xk Credits MIT Runge Kutta Derivation https://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node5.html Atomic Vibration Clip (electrons technically) https://www.youtube.com/watch?v=ofp-OHIq6Wo NASA Hurricane Video https://youtu.be/p-3aB9hJ8Hc?si=qha6kCicKlDLHOxo Solar System Clip https://youtu.be/z8aBZZnv6y8?si=3VX2OkpMlKOix76k

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