MATLAB: Solving Coupled Ordinary differential equations with unknown constants in the equation

coupled ordinary differential equationsdifferential equations with unknown constantsnonlinear differential equationnumerical integration

Hi , I have two second order nonlinear coupled ordinary differential equations to be solved. If the differential equations are set up well, I can solve it using the initial conditions using one of Matlab's ODE solvers. Instead I have two unknown parameters in the differential equation. But, I know two values of the four element state vector at the end. These have to be used to get the two unknown parameters in the differential equation. How do I proceed? For example, y'' = t^2+ay^2+bxy; x'' = ty''/(1+x); where a and b are the unknowns here and the equations have to be solved from [0,T]; x(0),y(0),x'(0),y'(0),x(T) and y(T) are known. So how to get a and b?

Best Answer

Take a look at the example
"Compute Fourth Eigenvalue of Mathieu's Equation"
under
https://de.mathworks.com/help/matlab/ref/bvp4c.html
It shows how to estimate one parameter of a second-order ODE given three boundary conditions. It should be no problem to use this example for your case (estimate 2 parameters given 6 boundary conditions).
Best wishes
Torsten.
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