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Julia: Solving ODEs with Euler, RK4, and DifferentialEquations

#julialang #packages #programming Solving Differential Equations is an aspect used constantly throughout a scientist's career. In the pure/applied math areas, we try to solve these equations analytically, but sometimes we don't have an analytical solution. This is where a computational background comes in to help for solving DEs. I first go into Euler's method which is pretty much taught at a calculus/DE level, and then expand to the Runge-Kutta-4 (RK4) which can be considered the work horse of academia. I also go into the DifferentialEquations library which has TONS of methods to solve out all different types of DEs out there, and really one video wouldn't be robust enough to cover the full functionality of this library. These examples cover ordinary linear DEs, because it is a good starting point for solving DEs, but later we will look at more obscure cases. SECTIONS ----------------- 0:00 - Boiler Plate Code 0:37 - Euler's Method 2:30 - RK4 Method 3:52 - Solve One ODE Function (DE Library) 7:02 - Solve a System ODE (DE Library) DifferentialEquations ---------------------------------- https://diffeq.sciml.ai/stable/ Numerical Repo -------------------------- https://github.com/da-james/numerical... Learning Repo ----------------------- https://github.com/da-james/djs-offic... IG:   / djsofficehours   TT:   / djsofficehours   T:   / djsofficehours