Two classes of explicit generalized runge-kutta processes for non- stiff systems of ordinary differential equations

References

• Butcher , J.C. 1963 . Coefficients for the study of Runge Kutta processes . J. Austral. Math. Soc , 3 : 185 – 201 .
   Google Scholar
• Day , J.D. 1980 . On Generalized Runge-Kutta Methods , University of Queensland . Ph.D. Thesis, Dept. of Mechanical Engineering
   Google Scholar
• England , R. 1969 . Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations . Comput. J , 12 : 166 – 170 .
   Google Scholar
• Fehlberg , E. 1969 . Low order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems . NASA Tech. Rep , R-315
   Google Scholar
• Forsythe , G.E. , Malcolm , M.A. and Moler , C.B. 1977 . Computer Methods for Mathematical Computations , Englewood Cliffs, N.J : Prentice-Hall .
   Google Scholar
• Van Der Houwen , P.J. 1972 . Explicit and semi-implicit Runge-Kutta formulas for the integration of stiff equations , Amsterdam : Mathematisch Centrum . Report TW132
   Google Scholar
• Van Der Houwen , P.J. 1976 . Construction of Integration Formulas for Initial value Problems , Amsterdam : North Holland .
   Google Scholar
• Hull , T.E. , Enright , W.H. , Fellen , B.M. and Sedgwick , A.E. 1972 . Comparing numerical methods for ordinary differential equations . SIAM J. Numer. Anal , 9 : 603 – 637 .
   Web of Science ®Google Scholar
• Lambert , J.D. 1973 . Computational Methods in Ordinary Differential Equations , London : Wiley .
   Google Scholar
• Lapidus , L. and Seinfeld , J.H. 1971 . Numerical Solution of Ordinary Differential Equations , New York : Academic Press .
   Google Scholar
• Norsett , S.D. and Wolfbrandt , A. 1979 . Order conditions for Rosenbock type methods . Numer. Math , 32 : 1 – 15 .
   Google Scholar
• Verwer , J.G. 1977 . S-Stability properties for Generalized Runge-Kutta methods . Numer.Math , 27 : 359 – 370 .
   Google Scholar