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Implementing second-derivative multistep methods using the Nordsieck polynomial representation. (English) Zbl 0385.65034


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65D30 Numerical integration
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[1] Germund G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informations-Behandling 3 (1963), 27 – 43. · Zbl 0123.11703
[2] W. H. Enright, Second derivative multistep methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 11 (1974), 321 – 331. · Zbl 0249.65055 · doi:10.1137/0711029
[3] W. H. ENRIGHT (1974b), ”Optimal second derivative methods for stiff systems,” in Stiff Differential Systems, R. A. Willoughby (Editor), Plenum Press, New York, pp. 95-109.
[4] W. H. ENRIGHT, T. E. HULL & B. LINDBERG (1975), ”Comparing numerical methods for stiff systems of ODE:s,” BIT, v. 15, pp. 10-48. · Zbl 0301.65040
[5] C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. · Zbl 1145.65316
[6] Y. Genin, An algebraic approach to \?-stable linear multistep-multiderivative integration formulas, Nordisk Tidskr. Informationsbehandling (BIT) 14 (1974), 382 – 406. · Zbl 0322.65037
[7] G. K. Gupta, Some new high-order multistep formulae for solving stiff equations, Math. Comp. 30 (1976), no. 135, 417 – 432. · Zbl 0332.65046
[8] Rolf Jeltsch, Note on \?-stability of multistep multiderivative methods, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), no. 1, 74 – 78. · Zbl 0321.65043
[9] J. D. Lambert, Computational methods in ordinary differential equations, John Wiley & Sons, London-New York-Sydney, 1973. Introductory Mathematics for Scientists and Engineers. · Zbl 0258.65069
[10] J. D. Lambert and S. T. Sigurdsson, Multistep methods with variable matrix coefficients, SIAM J. Numer. Anal. 9 (1972), 715 – 733. · Zbl 0246.65024 · doi:10.1137/0709060
[11] W. Liniger and F. Odeh, \?-stable, accurate averaging of multistep methods for stiff differential equations, IBM J. Res. Develop. 16 (1972), 335 – 348. Mathematics of numerical computation. · Zbl 0272.65050 · doi:10.1147/rd.164.0335
[12] Werner Liniger and Ralph A. Willoughby, Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Numer. Anal. 7 (1970), 47 – 66. · Zbl 0187.11003 · doi:10.1137/0707002
[13] Matti Mäkelä, Olavi Nevanlinna, and Aarne H. Sipilä, Exponentially fitted multistep methods by generalized Hermite-Birkhoff interpolation, Nordisk Tidskr. Informationsbehandling (BIT) 14 (1974), 437 – 451. · Zbl 0278.65079
[14] G. J. Makinson, Stable high order implicit methods for the numerical solution of systems of differential equations, Comput. J. 11 (1968/1969), 305 – 310. · Zbl 0167.15704 · doi:10.1093/comjnl/11.3.305
[15] Arnold Nordsieck, On numerical integration of ordinary differential equations, Math. Comp. 16 (1962), 22 – 49. · Zbl 0105.31902
[16] C. S. Wallace and G. K. Gupta, General linear multistep methods to solve ordinary differential equations, Austral. Comput. J. 5 (1973), 62 – 69. · Zbl 0265.65039
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