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

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
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References:

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