Simultaneously numerically integrate coupled ODE's in MATLAB
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In MATLAB, I need to numerically integrate two ODE's. Say I have variables time 't', x1(t) and x2(x1).
First differeential equation: contains dervative with respect to x1
Second differeential equation: contains dervative with respect to time 't'
time doesn't explicitly occur in either equation.
But since these are coupled equations, how do I simultaneously integrate at least numerically in MATLAB.
Teja Muppirala on 28 Dec 2017
You can get dx2/dt by multiplying dx2/dx1 * dx1/dt.
As a simple example say (I'll use x and y instead of x1 and x2 cause it's easier to see):
dy/dx = x
dx/dt = t
Then the analytic solution (ignoring integration constants) is
x = t^2/2
y = x^2/2 = t^4/8
You can verify that dy/dt = t^3/2 = x*t = dy/dx * dx/dt.
So, the equations you'd put into the ODE solver would be:
dy/dt = x*t
dx/dt = x