How to solve a system of nonlinear 2nd order differential equations?
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Hi there,
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);
% etc
% 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
댓글 수: 7
Babak
2013년 3월 4일
I think after your write your equations in the form I'm mentioning above, you can solve it with any ODE solver like ODE45. It doesn't seem to be a complicated case.
답변 (2개)
Babak
2013년 2월 21일
You need to use the optimization toolbox and it's fsolve(.) routine. You can embed all your nonlinear functions (can be an integrated ODE or whatever)as the arguments of fsolve, assigning thos functions to be the ones that are needed to be optimized.
Franziska
2013년 3월 2일
댓글 수: 1
Alessandro Antonini
2013년 6월 1일
I need to solve a system of 3 equations in the variable x1,x2,x3, I do not know how write the ode function that takes into account a term of a second order derivative of x2 in equation 1. I have a system like that:
ddx1=F1(t)-B1*dx1-M3*ddx3-B3*dx3-M2*ddx2-B2*dx2
ddx2=F2(t)-B2*dx2-K2*dx-M1*ddx1-B1*dx1-M2*ddx2-B2*dx2
ddx2=F3(t)-B3*dx3-K3*dx3-M1*ddx1-B1*dx1-K1*dx1-M2*ddx2-B2*dx2
I do not know how write in the ode function for this system. Can you please explain o write an example of the ode function required to solve a non linear system like that? I would be greateful
Best regards Alessandro Antonini
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