MATLAB: Ode45

numerical integrationode45

Hi, Having solved a second order equation of motion using ode45 function i wonder how could i modify the function to solve a whole system of equations in matrix form [A]{xdoubledot}+[B]{xdot}+[c]{x}={p(t)}, instead of solving individual equations for x vector variables. Would that be possible ?

Best Answer

Yes, certainly possible. The basic approach would be to turn it into a system of first order odes of twice the dimension as follows (where x and xdot are vectors):
y1 = x
y2 = xdot
then, if A is invertible
y1' = y2
y2' = A \ (-B*y2 - c*y1 + p(t))
You'd then write a file to implement this in MATLAB like this
function dy = myode(t, y)
  n = numel(y)/2;
  y1 = y(1:n);
  y2 = y(n+1:2*n);
  dy = [y2; A \ (-B*y2 - c*y1 + p(t))
end
and solve it with ode45 (or whichever solver happens to be most suitable) as usual.
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