• Main page for Runge-Kutta schemes

Order conditions for an order 7 Runge-Kutta scheme - RKcoeff7a.mws

• Order conditions for an order 7 Runge-Kutta scheme and their associated rooted trees.

Derivation of 10 stage, combined order 6 and 7 Runge-Kutta schemes - RKcoeff7b.mws

• Jim Verner's "most robust" and "most efficient" schemes etc.
   
• Coefficients for the schemes and some properties
  RKcoeff7b_1.pdf     RKcoeff7b_2.pdf     RKcoeff7b_3.pdf     RKcoeff7b_4.pdf     RKcoeff7b_5.pdf     RKcoeff7b_6.pdf

Derivation of 11 stage, order 7 Runge-Kutta schemes, each with a 12 stage order 6 FSAL embedded scheme - RKcoeff7c.mws

• A scheme due to Philip Sharp and Jim Verner together with similar schemes.
  See: "Completely Imbedded Runge-Kutta Pairs", by P. W. Sharp and J. H. Verner,
           SIAM Journal on Numerical Analysis, Vol. 31, No. 4. (Aug., 1994), pages 1169 to 1190.
   
• Coefficients for the schemes and some properties
  RKcoeff7c_1.pdf     RKcoeff7c_2.pdf     RKcoeff7c_3.pdf     RKcoeff7c_4.pdf     RKcoeff7c_5.pdf     RKcoeff7c_6.pdf

Derivation of 10 stage, order 7 Runge-Kutta schemes, each with an embedded order 6 scheme - RKcoeff7d.mws

• Some schemes due to Tanaka, Muramatsu and Yamashita together with similar schemes.
  See: On the Optimization of Some Nine-Stage Seventh-order Runge-Kutta Method, by M. Tanaka, S. Muramatsu and S. Yamashita,
          Information Processing Society of Japan, Vol. 33, No. 12 (1992) pages 1512-1526.
   
• Coefficients for the schemes and some properties
  RKcoeff7d_1.pdf     RKcoeff7d_2.pdf     RKcoeff7d_3.pdf     RKcoeff7d_4.pdf

Derivation of 11 stage, combined order 6 and 7 Runge-Kutta schemes- RKcoeff7e.mws

• A scheme due to P. Sharp and E. Smart together with similar schemes.
  See: Explicit Runge-Kutta Pairs with One More Derivative Evaluation than the Minimum, by P.W.Sharp and E.Smart,
  Siam Journal of Scientific Computing, Vol. 14, No. 2, pages. 338-348, March 1993.
   
• Coefficients for the schemes and some properties
  RKcoeff7e_1.pdf     RKcoeff7e_2.pdf     RKcoeff7e_3.pdf     RKcoeff7e_4.pdf     RKcoeff7e_5.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

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