- #1
karlzr
- 131
- 2
The equation looks like: ##x''(t)+b x'(t)+cx(t)+ d x^3(t)=0##. This is the motion of a particle in a potential ##cx^2/2+d x^4/4## with friction force ## b x'##. In my case, the friction term is very small and the particle will oscillate billions of times before the magnitude decreases significantly. So how do we solve this kind of equations to a very late final moment when the magnitude almost dies out?
Mathematica or Matlab doesn't work because of the stiffness problem, i.e. the particle oscillates so fast that we need to set the step size extremely small in order to have reliable numerical result. Another difficulty is the potential energy is not symmetric around the minimum. Thus I guess we cannot use the approximate form for the solution :##y(x)=A(t) cos (\omega(t)t)##.
Thanks a lot for any kind of suggestion!
Mathematica or Matlab doesn't work because of the stiffness problem, i.e. the particle oscillates so fast that we need to set the step size extremely small in order to have reliable numerical result. Another difficulty is the potential energy is not symmetric around the minimum. Thus I guess we cannot use the approximate form for the solution :##y(x)=A(t) cos (\omega(t)t)##.
Thanks a lot for any kind of suggestion!