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Families of methods for ordinary differential equations based on trigonometric polynomials. (English) Zbl 0529.65050


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
42A10 Trigonometric approximation

Citations:

Zbl 0163.390

Software:

MACSYMA
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bogen, R., (MACSYMA Reference Manual (1975), MIT Press: MIT Press Cambridge, MA)
[2] Brock, P.; Murray, F. J., The use of exponential sums in step by step integration, Math. Tables Aids Comput., 6, 63-78 (1952) · Zbl 0046.34301
[3] Dennis, S. C.R., The numerical integration of ordinary differential equations possessing exponential type solutions, (Proc. Cambridge Phil. Soc., 65 (1960)), 240-246 · Zbl 0095.31805
[4] Gautschi, W., Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math., 3, 381-397 (1961) · Zbl 0163.39002
[5] Lambert, J. D., Computational Methods in Ordinary Differential Equations (1977), Wiley: Wiley London · Zbl 0258.65069
[6] Lambert, J. D.; Watson, I. A., Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl., 18, 189-202 (1976) · Zbl 0359.65060
[7] Stiefel, E.; Bettis, D. G., Stabilization of Cowell’s method, Numer. Math., 13, 154-175 (1969) · Zbl 0219.65062
[8] Urabe, M.; Mise, S., A method of numerical integration of analytic differential equations, J. Sci. Hiroshima Univ. Ser. A, 19, 307-320 (1955) · Zbl 0067.35701
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