How to solve a system of nonlinear 2nd order differential equations?
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I have a challenge solving a system of differential equations 2nd order. I do not receive an error message but have rather strange results... Could you please have a look on what I did and comment on it. If you think the way it was done is fine, I may have the bug some where else...
function dHbar = diffH(tspan,H)
h1 = H(1);
dh1 = H(2);
ddh1 = H(3);
h2 = H(4);
dh2 = H(5);
ddh2 = H(6);
h3 = H(7);
dh3 = H(8);
ddh3 = H(9);
% the equations are very long. In short the look similar to the following where f(h1,dh1) means some expression as a function of ...
% A1 to A3 are known
ddh1 = ( A1 * f(h1,dh1) + A2 * f(h2,dh2,ddh2) + A3 * f(h3,dh3,ddh3));
ddh2 = ( A2 * f(h2,dh2) + A1 * f(h1,dh1,ddh1) + A3 * f(h3,dh3,ddh3));
ddh3 = ( A3 * f(h3,dh3) + A1 * f(h1,dh1,ddh1) + A2 * f(h2,dh2,ddh2));
dHbar = [h1; dh1; ddh1; h2; dh2; ddh2; h3; dh3; ddh3];
Then I call it with
[T,Hbar] = ode45('diffH',tspan,H); % with tspan - time and H - starting values
As mentioned above, I receive some solution, but it seems strange.
Thanks a lot for your help in advance. Cheers, Franziska