/usr/share/doc/rheolef-doc/examples/runge_kutta_semiimplicit.icc is in rheolef-doc 6.7-6.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | // see WanShuZha-2015 page 212
namespace rk {
constexpr size_t pmax = 3;
const Float _g2 = 1 - 1/sqrt(Float(2));
const Float _d2 = 1 - 1/(2*_g2);
const Float _g3 = 0.435866521508459;
const Float _b31 = -3*(_g3*_g3)/2 + 4*_g3 - 1./4;
const Float _b32 = 3*(_g3*_g3)/2 - 5*_g3 + 5./4;
const Float _a31 = -0.356;
const Float _a32 = (1/Float(3) - 2*(_g3*_g3) - 2*_b32*_a31*_g3)/(_g3*(1-_g3));
Float alpha[][pmax+1][pmax+1]
= { {},
{ {0},
{0, 1} },
{ {0},
{0, _g2},
{0, 1-_g2, _g2} },
{ {0},
{0, _g3},
{0, (1-_g3)/2, _g3},
{0, _b31, _b32, _g3} } };
Float tilde_alpha[][pmax+1][pmax+1]
= { {},
{ {},
{1} },
{ {},
{_g2},
{_d2, 1-_d2} },
{ {},
{_g3},
{(1+_g3)/2 - _a31, _a31},
{0, 1-_a32, _a32} } };
Float beta [][pmax+1]
= { {},
{0, 1},
{0, 1-_g2, _g2},
{0, _b31, _b32, _g3} };
Float tilde_beta [][pmax+1]
= { {},
{1},
{_d2, 1-_d2, 0},
{0, _b31, _b32, _g3} };
Float gamma [][pmax+1]
= { {},
{0, 1},
{0, _g2, 1},
{0, _g3, (1+_g3)/2, 1} };
} // namespace rk
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