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Original Articles

Efficient eighth order p-stable methods for second order initial value problems

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Pages 119-151 | Received 08 Nov 1995, Published online: 20 Jan 2011

References

  • Cash , J. R. 1981 . High order P-stable formulae for the numerical integration of periodic initial value problems . Numer. Math. , 37 : 355 – 370 .
  • Cooper , G. J. and Butcher , J. C. 1983 . An iteration scheme for implicit Runge-Kutta methods . IMA J. Numer. Anal. , 3 : 127 – 140 .
  • Gladwell , I. and Thomas , R. M. 1983 . Damping and phase analysis for some methods for solving second order ordinary differential equations . Int. J. Num. Meth. in Engng. , 19 : 495 – 503 .
  • Khiyal M. S. H. Efficient algorithms based on direct hybrid methods for second order initial value problems. Ph. D Thesis. UMIST Manchester 1991
  • Lambert , J. D. and Watson , I. A. 1976 . Symmetric multistep methods for periodic initial value problems . J. Inst. Maths. Applics. , 18 : 189 – 202 .
  • Thomas , R. M. 1987 . Efficient fourth order P-stable formulae . BIT , 24 : 599 – 614 .
  • Thomas R. M. Khiyal M. S. H. High order, P-stable methods for nonlinear oscillation problems. University of Manchester/UMIST Numerical Analysis Report No.221 1992

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