How to solve the system of two second order differential equations?:
x''(t)=f(x',x,y',y,t),\qquad y''(t)=g(x',x,y',y,t)
Is there any numerical method, algorithm?
How to solve the system of two second order differential equations?:
x''(t)=f(x',x,y',y,t),\qquad y''(t)=g(x',x,y',y,t)
Is there any numerical method, algorithm?
The usual trick is to write this system as a first-order one by setting U=(U_1,U_2,U_3,U_4)=(X,Y,X',Y') and getting U'=(U_3,U_4,f(U_3,U_1,U_4,U_2,t),g(U_3,U_1,U_4,U_2,t)) = F(U,t) Then you can use any of the several goods numerical methods, such as Runge–Kutta.