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Original Articles

New runge kutta starters for multistep methods

Starters for multistep methods

&
Pages 99-104 | Received 15 Nov 1997, Published online: 20 Mar 2007

References

  • Evans , D. J. and Yakkub , A. R. 1995 . A New Fourth Order Runge-Kutta Method Based on the Contraharmonic Mean Formula . Intern. J. Computer Math , 57 : 249 – 256 . Loughborough University of Technology, Department of Computer Studies, Report No. 849. [Contributed Talks at the Vl-th SERC Numerical Analysis Summer School Leicester University. 25-29 July 1994]
  • Evans , D. J. and Yaakub , A. R. 1993 . A New 4th Order Runge-Kutta Method Based on the Centroidal Mean Formula , Loughborough University of Technology .
  • Evans , D. J. and Yaakub , A. R. 1996 . A New Fifth Order Weighted Runge-Kutta Formula, Loughborough University of Technology, Department of Computer Studies, Report No. 989 . Intern. J. Computer Math , 00 : 1 – 17 . in press 1995
  • Evans , D. J. and Yaacob , N. 1994 . A Fourth Order Runge-Kutta Method Based on the Heronian Mean Formula, Lougborough University of Technology, Department of Computer Studies, Report No. 879
  • Evans , D. J. and Sanugi , B. B. 1987 . A New 4th Order Runge-Kutta Method for Initial Value Problems , Edited by: Fatunla , S. O. Dublin : Boole Press . Computational Mathematics II
  • Gear , C. W. 1980 . Runge-Kutta Starters For Multistep Methods . ACM Transactions on Mathematical Software , 6 ( 3 ) : 263 – 279 .
  • Hindmarsh , A. C. 1974 . GEAR: Ordinary Differential Equation Solver , Livermore, , California : Lawrence Livermore Lab . Rep. UCID– 30001, Rev. 3
  • Krogh , F. T. 1972 . VGDQ/SVDQ/DVDQ-Variable Order Integrators for the Numerical Solution of Ordinary Differential Equations , Vol. 314 , Pasadena, , California : Jet Propulsion Lab . Subroutine Write-up
  • Lambert , J. D. 1991 . Numerical Methods for Ordinary Differential Systems , London : John Wiley and Sons .
  • Sanugi , B. B. and Evans , D. J. 1993 . A New Fourth Order Runge-Kutta Formula Based on Harmonic Mean, Loughborough University of Technology, Department of Computer Studies, Report No. 799
  • Shampine , L. F. and Gordon , M. K. 1975 . Computer Solution of Ordinary Differential Equations: The Initial Value Problem , San Francisco : Freeman .
  • Yaakub , A. R. and Evans , D. J. 1993 . A New Fourth Order Runge-Kutta Methods Based on the Root Mean Square Formula, Loughborough University of Technology, Department of Computer Studies, Report No. 862

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