Numerically Integrating Differential Equations in Excel and Python: Runge Kutta Method

I want to go over an implementation of the 4th-order Runge Kutta algorithm in both Python and Excel. This algorithm is used extensively in scientific computing. MATLAB’s ODE45 solver, as well as the solve_ivp function from Scipy use a variation of this technique. The goal of this video is to show how simple it is to make use of this method when one doesn’t gave access to canned routines such as those in MATLAB or Scipy. This video was inspired by an engineer I worked with years ago who ran into this issue. He had an ODE to solve, but the only software he had easy access to was Excel.