I have a problem that requres taking a second order ODE and decomposing it into 2 first-order ODEs, then approximating a solution using Euler's explicit method. I already did the decomposition:
Here are the resultant ODEs:
y1' = y2
y2' = [ (5000+80t-0.161y2^2)*(32.2/(3000-80t)) ]
As you can see I have one dependent varialble y, and one independent variable t.
My question is how to write an Euler function file with 2 equations. I have an Euler function file from a textbook that takes care of a single ODE, but I want to solve a system of coupled ODEs. Below is the Euler code from the textbook for a single ODE, but I don't even know where to start in terms of writing my own code.
% function file
function [x, y] = odeEULER(ODE,a,b,h,yINI) x(l) = a; y(l) = yINI; N = (b - a)/h; for i = l:N x(i + 1) = x(i) + h; y(i + 1) = y(i) + ODE(x(i) ,y(i))*h; end end
Best Answer