Rheolef  7.2
an efficient C++ finite element environment
 
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runge_kutta_semiimplicit.icc
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1
25namespace rk {
26 // see WanShuZha-2015 page 212
27 constexpr size_t pmax = 3;
28 const Float _g2 = 1 - 1/sqrt(Float(2));
29 const Float _d2 = 1 - 1/(2*_g2);
30 const Float _g3 = 0.435866521508459;
31 const Float _b31 = -3*(_g3*_g3)/2 + 4*_g3 - 1./4;
32 const Float _b32 = 3*(_g3*_g3)/2 - 5*_g3 + 5./4;
33 const Float _a31 = -0.356;
34 const Float _a32 = (1/Float(3) - 2*(_g3*_g3) - 2*_b32*_a31*_g3)/(_g3*(1-_g3));
36 = { {},
37 { {0},
38 {0, 1} },
39 { {0},
40 {0, _g2},
41 {0, 1-_g2, _g2} },
42 { {0},
43 {0, _g3},
44 {0, (1-_g3)/2, _g3},
45 {0, _b31, _b32, _g3} } };
46
48 = { {},
49 { {},
50 {1} },
51 { {},
52 {_g2},
53 {_d2, 1-_d2} },
54 { {},
55 {_g3},
56 {(1+_g3)/2 - _a31, _a31},
57 {0, 1-_a32, _a32} } };
58
60 = { {},
61 {0, 1},
62 {0, 1-_g2, _g2},
63 {0, _b31, _b32, _g3} };
65 = { {},
66 {1},
67 {_d2, 1-_d2, 0},
68 {0, _b31, _b32, _g3} };
70 = { {},
71 {0, 1},
72 {0, _g2, 1},
73 {0, _g3, (1+_g3)/2, 1} };
74} // namespace rk
see the Float page for the full documentation
const Float _b32
Float tilde_alpha[][pmax+1][pmax+1]
const Float _d2
const Float _g3
const Float _a31
Float tilde_beta[][pmax+1]
const Float _b31
Float gamma[][pmax+1]
Float beta[][pmax+1]
Float alpha[][pmax+1][pmax+1]
const Float _a32
constexpr size_t pmax
const Float _g2