# TSBASICSYMPLECTIC
ODE solver using basic symplectic integration schemes These methods are intended for separable Hamiltonian systems
```none
  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
```none
  H(q,p,t) = T(p,t) + V(q,t).
```


As a result, the system can be genearlly represented by
```none
  qdot = f(p,t) = dT(p,t)/dp
  pdot = g(q,t) = -dV(q,t)/dq
```


and solved iteratively with
```none
  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
 [](chapter_ts), `TSCreate()`, `TSSetType()`, `TSRHSSplitSetIS()`, `TSRHSSplitSetRHSFunction()`, `TSType`

## Level
beginner

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c.html#TSBASICSYMPLECTIC">src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c</A>


---
[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c)


[Index of all TS routines](index.md)  
[Table of Contents for all manual pages](/docs/manualpages/index.md)  
[Index of all manual pages](/docs/manualpages/singleindex.md)  
