Maple worksheets on the derivation of order 12 Runge-Kutta schemes
Derivation of 25 stage, order 12 Runge-Kutta schemes - RKcoeff12a.mws RKcoeff12b.mws RKcoeff12c.mws RKcoeff12d.mws
Derivation of embedded order 9 schemes for order 12 Runge-Kutta methods - RKcoeff12a_(9).mws RKcoeff12c_(9).mws RKcoeff12d_(9).mws
Derivation of embedded order 10 and 11 schemes for an order 12 Runge-Kutta method - RKcoeff12a_(10,11).mws
- Defective embedded order 10 and 11 schemes for Terry Feagin's order 12 scheme
Derivation of 25 stage, order 12 Runge-Kutta schemes - RKcoeff12e.mws RKcoeff12f.mws RKcoeff12g.mws RKcoeff12h.mws
- Hiroshi Ono's scheme and some modifications of his scheme.
See: "On the 25 stage 12th order explicit Runge-Kutta method", by Hiroshi Ono.
Transactions of the Japan Society for Industrial and Applied Mathematics, Vol. 6, No. 3, (2006) pages 177 to 186.
- Coefficients for the schemes and some properties
RKcoeff12e_1.pdf RKcoeff12f_1.pdf RKcoeff12g_1.pdf RKcoeff12h_1.pdf
Derivation of an embedded order 9 scheme for an order 12 Runge-Kutta method - RKcoeff12h_(9).mws
Derivation of 31 stage, combined order 11 and 12 Runge-Kutta schemes - RKcoeff12k.mws RKcoeff12m.mws RKcoeff12n.mws
Procedures related to the construction of Runge-Kutta schemes - butcher.zip
Procedures for root-finding and determining minimum points - roots.zip
Procedures for numerical integration - intg.zip
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