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On accuracy and unconditional stability of linear multistep methods for second order differential equations. (English) Zbl 0378.65043


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
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[1] G. Dahlquist,A special stability problem for linear multistep methods, BIT 3 (1963), 27–43. · Zbl 0123.11703 · doi:10.1007/BF01963532
[2] G. Dahlquist,On the relation of G-stability to other stability concepts for linear multistep methods, inTopics in Numerical Analysis III, ed. J. J. H. Miller, Academic Press, 1977. · Zbl 0438.65073
[3] A. Dinghas,Vorlesungen über Funktionentheorie, Springer Verlag, 1961. · Zbl 0102.29301
[4] Y. Genin,A new approach to the synthesis of stiffly stable linear multistep methods, IEEE Trans. on Circuit Theory, 20 (1973), 352–360. · doi:10.1109/TCT.1973.1083700
[5] R. D. Grigorieff,Numerik gewöhnlicher Differentialgleichungen, vol. 2, Teubner Verlag, 1977.
[6] J. Lambert and I. A. Watson,Symmetric multistep methods for periodic initial value problems, J. Inst. Maths. Applics. 18 (1976), 189–202. · Zbl 0359.65060 · doi:10.1093/imamat/18.2.189
[7] R. Richtmyer and K. W. Morton,Difference Methods for Initial-Value Problems, 2nd ed., Interscience Publishers, 1967. · Zbl 0155.47502
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