Help in second order ode numeric solution

[Johnbasko]

Dear all,

Im trying to solve the following ode:

y'' = -0.12*y + 0.4/sqrt(y^2 + 5.76) , y=y(t) , t: [-50,50]
y(-50)=2.3 , y'(-50)=0

i changed it to a set of two first order ode using z=y'
and solve it with finite differences.

note that the right side doesn't depend on t.

the solution start good and raise till a pick point and than decay till zero, the problem it that when it decay to zero, infact i received again that y=y'=z=0 meaning I am reaching my initial point and than the solution raise again to a pick point and decay again to zero etc etc...

the real solution should raise , reach the pick when t=0 and decay again to zero till t=50.

how can i solve that issue and stop the periodic behaviour when it decay to zero ?

thanks a lot

 

[gtoguy97]

The issue you are facing is likely due to the numerical method you are using for solving the ODE. Finite differences is not the best method for solving this type of ODE as it is not very accurate. You should consider using a higher order numerical method such as Runge-Kutta, which is more accurate and can provide you with better results. Alternatively, you could also try using a symbolic solver such as Mathematica or Maple to solve the ODE analytically.