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Table 1
Four-stage GRK4(3)T method.
| Mu1 = hS(u0) | |
| M(u2 + b21u1) = hS(u0 + a21u1) + b21u1 | |
| M(u3 + b31u1 + b32u2) = hS(u0 + a31u1 + a32u2) | |
| + b31u1 + b32u2 | |
| M(u4 + b41u1 + b42u2 + b43u3) = hS(u0 + a31u1 + a32u2) | |
| + b41u1 + b42u2 + b43u3 | |
|
|
| method coefficients | |
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|
|
| ξ = 0.231 | |
| a21 = 0.462 | a31 = −0.0815668168327 |
| a32 = 0.961775150166 | |
| b21 = −1.1715570032554 | b31 = 1.3474220056017 |
| b32 = 0.036902408159394 | b41 = 1.2243152902338 |
| b42 = −1.982508585632 | b43 = −0.48142135641991 |
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|
|
| c1 = 0.217487371653 | c2 = 0.486229037990 |
| c3 = 0 | c4 = 0.296283590357 |
Notes. M = I−hξJ(u0) with u0 = u(tn) and internal step-size h.
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