TSBASICSYMPLECTIC#

ODE solver using basic symplectic integration schemes These methods are intended for separable Hamiltonian systems

  qdot = dH(q,p,t)/dp
  pdot = -dH(q,p,t)/dq

where the Hamiltonian can be split into the sum of kinetic energy and potential energy

  H(q,p,t) = T(p,t) + V(q,t).

As a result, the system can be genearlly represented by

  qdot = f(p,t) = dT(p,t)/dp
  pdot = g(q,t) = -dV(q,t)/dq

and solved iteratively with

  q_new = q_old + d_i*h*f(p_old,t_old)
  t_new = t_old + d_i*h
  p_new = p_old + c_i*h*g(p_new,t_new)
  i=0,1,...,n.

The solution vector should contain both q and p, which correspond to (generalized) position and momentum respectively. Note that the momentum component could simply be velocity in some representations. The symplectic solver always expects a two-way splitting with the split names being “position” and “momentum”. Each split is associated with an IS object and a sub-TS that is intended to store the user-provided RHS function.

Reference#

  • **** -*** wikipedia (https://en.wikipedia.org/wiki/Symplectic_integrator)

See Also#

TS: Scalable ODE and DAE Solvers, TSCreate(), TSSetType(), TSRHSSplitSetIS(), TSRHSSplitSetRHSFunction(), TSType

Level#

beginner

Location#

src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c

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Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages