Some new high-order multistep formulae for solving stiff equations
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- by G. K. Gupta PDF
- Math. Comp. 30 (1976), 417-432 Request permission
Abstract:
Several new multistep formulae of orders up to 9 for solving stiff ordinary differential equations are presented. Results of numerical testing of these new formulae and some formulae presented in earlier papers and the stiff formulae used by Gear are included.References
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W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of O.D.E.’s," BIT, v. 15, 1975, pp. 10-48.
- W. H. Enright, Second derivative multistep methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 11 (1974), 321–331. MR 351083, DOI 10.1137/0711029
- C. W. Gear, The automatic integration of stiff ordinary differential equations. , Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968) North-Holland, Amsterdam, 1969, pp. 187–193. MR 0260180 C. W. GEAR, "Algorithm 407-DIFSUB for solution of ordinary differential equations," Comm. ACM, v. 14, 1971, pp. 185-190.
- G. K. Gupta and C. S. Wallace, Some new multistep methods for solving ordinary differential equations, Math. Comp. 29 (1975), 489–500. MR 373290, DOI 10.1090/S0025-5718-1975-0373290-5
- Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
- T. E. Hull, W. H. Enright, B. M. Fellen, and A. E. Sedgwick, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal. 9 (1972), 603–637; errata, ibid. 11 (1974), 681. MR 351086, DOI 10.1137/0709052 F. T. KROGH, "On testing a subroutine for the numerical integration of ordinary differential equations," J. ACM, v. 20, 1973, pp. 545-562.
- Bengt Lindberg, On smoothing and extrapolation for the trapezoidal rule, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 29–52. MR 281356, DOI 10.1007/bf01935326 N. MORRISON, Introduction to Sequential Smoothing and Prediction, McGraw-Hill, New York, 1969.
- C. S. Wallace and G. K. Gupta, General linear multistep methods to solve ordinary differential equations, Austral. Comput. J. 5 (1973), 62–69. MR 362919
- Olof B. Widlund, A note on unconditionally stable linear multistep methods, Nordisk Tidskr. Informationsbehandling (BIT) 7 (1967), 65–70. MR 215533, DOI 10.1007/bf01934126
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 417-432
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1976-0423812-1
- MathSciNet review: 0423812