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Maple worksheets on the derivation of order 9 Runge-Kutta schemes |
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Derivation of 16 stage, combined order 8 and 9 Runge-Kutta schemes - RKcoeff9a.mws
- Schems by Verner, Sharp and modifications of two schemes by Tsitouras.
See:
"Explicit Runge-Kutta methods with estimates of the Local Truncation Error", by J.H. Verner,
SIAM Journal of Numerical Analysis 1978, 772-790,
"High order explicit Runge-Kutta pairs for ephemerides of the Solar System and the Moon", by Philip W. Sharp,
Journal of Applied Mathematics & Decision Sciences, 4(2), 183-192 (2000),
"Optimized explicit Runge-Kutta pair of order 9(8)", by Ch. Tsitouras,
Applied Numerical Mathematics, 38 (2001) 123-134.
- Coefficients for the schemes and some properties
RKcoeff9a_1.pdf RKcoeff9a_2.pdf RKcoeff9a_3.pdf RKcoeff9a_4.pdf RKcoeff9a_5.pdfDerivation of 16 stage, combined order 8 and 9 Runge-Kutta schemes - RKcoeff9b.mws
- Two schemes of Tsitouras
See: "Optimized explicit Runge-Kutta pair of order 9(8)", by Ch. Tsitouras,
Applied Numerical Mathematics, 38 (2001) 123-134.
- Coefficients for the schemes and some properties
RKcoeff9b_1.pdf RKcoeff9b_2.pdfDerivation of 17 stage, combined order 8 and 9 Runge-Kutta schemes - RKcoeff9c.mws RKcoeff9d.mws
- A scheme of Philip Sharp and modifications of this scheme
See: "High order explicit Runge-Kutta pairs for ephemerides of the Solar System and the Moon", by Philip W. Sharp,
Journal of Applied Mathematics & Decision Sciences, 4(2), 183-192 (2000),
- Coefficients for the schemes and some properties
RKcoeff9c_1.pdf RKcoeff9c_2.pdf RKcoeff9c_3.pdf RKcoeff9c_4.pdf
RKcoeff9d_1.pdf RKcoeff9d_2.pdf RKcoeff9d_3.pdf
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
