# TSBasicSymplectic
ODE solver using basic symplectic integration schemes These methods are intened for separable Hamiltonian systems

```none
qdot = dH(q,p,t)/dp
```
```none
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
```
```none
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)
```
```none
t_new = t_old + d_i*h
```
```none
p_new = p_old + c_i*h*g(p_new,t_new)
```
```none
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
 `TSCreate()`, `TSSetType()`, `TSRHSSplitSetIS()`, `TSRHSSplitSetRHSFunction()`


## 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>


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[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)  
