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<< "KrancThorn.m";
groups = {{"ode_group", {a, b}}, {"evolved_group", {phi, pi}}};
derivatives =
{
PDstandard2nd[i_] -> StandardCenteredDifferenceOperator[1,1,i],
PDstandard2nd[i_, i_] -> StandardCenteredDifferenceOperator[2,1,i]
};
PD = PDstandard2nd;
initialSineCalc =
{
Name -> "initial_sine",
Schedule -> {"AT INITIAL"},
Equations ->
{
phi -> Sin[2 Pi (x - t)],
pi -> -2 Pi Cos[2 Pi (x - t)],
a -> 0, b -> 1
}
};
evolveCalc =
{
Name -> "calc_rhs",
Schedule -> {"in MoL_CalcRHS"},
Where -> Interior,
Equations ->
{
dot[phi] -> pi,
dot[pi] -> a Euc[ui,uj] PD[phi,li,lj],
dot[a] -> b,
dot[b] -> -a
}
};
CreateKrancThornTT[groups, ".",
"SimpleWaveODE",
Calculations -> {initialSineCalc, evolveCalc},
PartialDerivatives -> derivatives,
DeclaredGroups -> {"evolved_group"},
ODEGroups -> {"ode_group"}
];
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