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<div id="version" align=right><b>petsc-3.10.3 2018-12-18</b></div>
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<A NAME="TSBasicSymplectic"><H1>TSBasicSymplectic</H1></A>
ODE solver using basic symplectic integration schemes These methods are intened for separable Hamiltonian systems
<P>
<pre>
qdot = dH(q,p,t)/dp
</pre>
<pre>
pdot = -dH(q,p,t)/dq
</pre>
<P>
where the Hamiltonian can be split into the sum of kinetic energy and potential energy
<P>
<pre>
H(q,p,t) = T(p,t) + V(q,t).
</pre>
<P>
As a result, the system can be genearlly represented by
<P>
<pre>
qdot = f(p,t) = dT(p,t)/dp
</pre>
<pre>
pdot = g(q,t) = -dV(q,t)/dq
</pre>
<P>
and solved iteratively with
<P>
<pre>
q_new = q_old + d_i*h*f(p_old,t_old)
</pre>
<pre>
t_new = t_old + d_i*h
</pre>
<pre>
p_new = p_old + c_i*h*g(p_new,t_new)
</pre>
<pre>
i=0,1,...,n.
</pre>
<P>
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 <A HREF="../IS/IS.html#IS">IS</A> object and a sub-<A HREF="../TS/TS.html#TS">TS</A> that is intended to store the user-provided RHS function.
<P>
Reference: wikipedia (https://en.wikipedia.org/wiki/Symplectic_integrator)
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../TS/TSCreate.html#TSCreate">TSCreate</A>(), <A HREF="../TS/TSSetType.html#TSSetType">TSSetType</A>(), <A HREF="../TS/TSRHSSplitSetIS.html#TSRHSSplitSetIS">TSRHSSplitSetIS</A>(), <A HREF="../TS/TSRHSSplitSetRHSFunction.html#TSRHSSplitSetRHSFunction">TSRHSSplitSetRHSFunction</A>()
<BR>
<P>
<P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>beginner<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c.html#TSBasicSymplectic">src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c</A>
<BR><A HREF="./index.html">Index of all TS routines</A>
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<BR><A HREF="../singleindex.html">Index of all manual pages</A>
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