New interpolants for runge-kutta algorithms using second derivatives

References

• Enright , W. H. , Jackson , K. R. , Norsett , S. P. and Thomsen , P. G. 1986 . Interpolants for Runge-Kutta formulas . ACM Trans. Math. Soft. , 12 : 193 – 218 .
   Web of Science ®Google Scholar
• Fehlberg E. Low order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems 1969 NASA TR R-315
   Google Scholar
• Horn , M. K. 1983 . Fourth and fifth order scaled Runge-Kutta algorithms for treating dense output . SIAM J. Num. Anal. , 20 : 558 – 568 .
   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
• Papageorgiou , G. , Simos , Th. and Tsitouras , Ch. 1988 . Some new Runge-Kutta methods with interpolation properties and their application to the magnetic binary problem . Cel. Mec. , 44 : 167 – 177 .
   Google Scholar
• Shampine , L. F. , Watts , W. A. and Davenport , S. M. 1976 . Solving non-stiff ordinary differential equations—The state of the art . SIAM Rev. , 18 : 376 – 410 .
   Google Scholar
• Shampine , L. F. 1985 . Interpolation for Runge-Kutta methods . SIAM. J. Num. Anal. , 22 : 1014 – 1027 .
   Google Scholar
• Shampine , L. F. 1986 . Some practical Runge-Kutta formulas . Math. of Comput. , 46 : 135 – 150 .
   Web of Science ®Google Scholar