0
$\begingroup$

I desperately need to solve a coupled system of linear second order differential equations of the form:

$ a_1x''+ b_1x' + c_1y'' + d_1y' =0 $

$ a_2x'' + b_2x' + c_2y'' + d_2y' + e_2y = 0 $

initial conditions are :

$ y(0)=y_0, y'(0)=x(0)=x'(0)=0. $

x and y are displacement in time.

What method do you suggest for solving this system? Any suggestion will be appreciated!

Thanks!

$\endgroup$
  • $\begingroup$ Try writing it in matrix form and computing the matrix exponential. $\endgroup$ – cauchyproblem Jan 20 '16 at 18:29
  • $\begingroup$ @Moo to explain more detail the system I should say that the system is a motion equation for coupled (sway and roll; in hydrodynamic), there are solutions for diagonal mass matrix when M12=M21=0, but in my case all paramaters of mass matrix are non-zero value (m11, m12, m21 and m22). $\endgroup$ – P.Asg Jan 21 '16 at 12:25
0
$\begingroup$

In case of linear ODE with constant coefficients, it is known that the general solution is a linear combination of exponential functions on the form $k\,e^{r\,t}$ where the various values of $r$ , real or complex, are the roots of a polynomial equation. So, a method to solve the system is to presume of the form of particular solutions and determine the parameters of them, as done below :

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.