Maple worksheets on the derivation of order 9 Runge-Kutta schemes |

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.pdf

Derivation 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.pdf

Derivation 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

Proceduresrelated 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