Thread Subject: 3*x''+(10^-3)*x'+123*x=2*cos(3*t); x=x(t);initial conditions x(0)=0 and x'(0)=0

Hi everybody,

I need to solve the Cauchy problem written in the title box ( I paste it here again ):

3*x''+(10^-3)*x'+123*x=2*cos(3*t); x=x(t);initial conditions x(0)=0 and x'(0)=0.

I tried with Runge-Kutta method and it seems to work as the solution x(t) is the same that I can get solving the equation by myself.

I need to know if it would be better another method (eventually multistep one) and why it would be better (please don't just tell me 'cause it's faster or so...I need to know the why too).

As last thing I need to estimate the error committed with Runge-Kutta and the other method you are going to suggest to me.

Here is the list of the functions I have got and I can use:

1.ONE STEP: Euler,Heun,Runge-Kutta
2.MULTI STEP: Adams_Bashforth, MlineHamming and MlineSimpson

Please,I need urgent help.

I hope you will answer soon,just contact me directly at xxcarlo_rossixx@yahoo.it

Thank you all, Carlo