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Extension to non-autonomous Hamiltonian systems

Assume that the previous problem is extended to non-autonomous Hamiltonians. It is straightforward to modify the above subroutine for this case. In the template file rksub.mf, modify the first line to include time-dependence: 


         subroutine evalf(f,q,p,t)
The definition of f needs to be modified (the vector of first derivatives of ) to account for time-dependence of the Hamiltonian: 

 <* FortranAssign[ f,
      Flatten[{Outer[D,{H},pvars],- Outer[D,{H},qvars],D[H,t]}]
   ] *>
The dimension of f must also be increased: 

         f(<* 2 d + 1 *>)
The main routine should now includes a line to increment the time value at each intermediary stage: 

         t = t + c(i)*h
for . Finally a modified call to rksub.f is required 

         call rksub(f,q,p,t)
To take the template file approach to an extreme, we could even select an implicit or explicit Runge-Kutta method, depending upon some stiffness criteria implemented in Mathematica.

bondaren@thsun1.jinr.ru