Spectral methods using rational basis functions on an infinite interval. (English) Zbl 0615.65090

Boyd, John P.

J. Comput. Phys. 69, 112-142 (1987).

The author is concerned with solving differential equations defined on (- \(\infty,\infty)\) by first using the mapping \(y=L \cot (t)\), where L is a constant and then applying the Galerkin method. He extends earlier results [C. E. Grosch and S. A. Orszag, ibid. 25, 273-295 (1977; Zbl 0403.65050) and the author, ibid. 45, 43-79 (1982; Zbl 0488.65035)] giving the rigorous foundations of the approach and improving algorithms. As an illustration five numerical examples are presented.

Reviewer: J.Mika

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
41A20	Approximation by rational functions
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

spectral methods; Galerkin method; numerical examples

Citations:

Zbl 0403.65050; Zbl 0488.65035

References:

[1]	Grosch, C.E.; Orszag, S.A., J. comput. phys., 25, 273, (1977)
[2]	Boyd, J.P., J. comput. phys., 25, 43, (1982)
[3]	Boyd, J.P., SIAM J. numer. anal., (1987), in press
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[5]	Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and applications, Soc. ind. and appl. math., (1977), Philadelphia · Zbl 0412.65058
[6]	Morse, P.M.; Feshbach, H., Methods of theoretical physics, part II, (), 1210
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[14]	Higgins, J.R., Completeness and basis properties of sets of special functions, (1977), Cambridge Univ. Press Cambridge · Zbl 0351.42021
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[16]	Lund, J.R.; Riley, B.V., IMA J. numer. anal., 4, 83, (1984)
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[22]	Boyd, J.P., J. comput. phys., (1987), in press