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

Citations:

Zbl 0403.65050; Zbl 0488.65035
Full Text:

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 [4] Boyd, J.P., J. comput. phys., 57, 454, (1985) [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 [7] Boyd, J.P., J. comput. phys., 54, 382, (1984) [8] Abramowitz, M.; Stegun, I., () [9] Boyd, J.P., J. comput. phys., 64, 266, (1986) [10] Cain, A.B.; Ferziger, J.H.; Reynolds, W.C., J. comput. phys., 56, 272, (1984) [11] Strang, G.; Fix, G.J., An analysis of the finite element method, (), 265 · Zbl 0179.22501 [12] Stenger, F., SIAM rev., 23, 165, (1981) [13] Christov, C.I., SIAM J. appl. math., 42, 1337, (1982) [14] Higgins, J.R., Completeness and basis properties of sets of special functions, (1977), Cambridge Univ. Press Cambridge · Zbl 0351.42021 [15] Boyd, J.P., Monthly weather rev., 106, 1184, (1978) [16] Lund, J.R.; Riley, B.V., IMA J. numer. anal., 4, 83, (1984) [17] Bowers, K.; Lund, J., SIAM J. numer. anal., (1985), in press [18] Boyd, J.P., Physica, 21D, 227, (1986) [19] Boyd, J.P., Monthly weather rev., 106, 1192, (1978) [20] Gill, A.E., Numerical models of Ocean circulation, (1975), Nat. Acad. Sci Washington, D.C [21] Boyd, J.P.; Moore, D.W., Dyn. atmos. oceans, 10, 51, (1986) [22] Boyd, J.P., J. comput. phys., (1987), in press
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.