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The space-time Sinc-Galerkin method for parabolic problems. (English) Zbl 0643.65068
The authors develop an infinite-order space-time Galerkin method for a parabolic partial differential equation in one space dimension. The basis functions of the method are sinc-functions composed with conformal maps. The Galerkin technique is employed simultaneously in space and time. It is shown that the method possesses exponential rate of convergence, ease of assembly of the discrete system, a global approximation and the ability to handle singular problems. The presented method does not have any restriction with regard to a largest time computation as this method provides global approximation to the solutions.
Reviewer: S.C.Rajvanshi

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
Full Text: DOI
[1] and , Fundamental Concepts in the Numerical Solution of Differential Equations, Wiley, New York, 1983.
[2] Evans, Int. j. numer. methods eng. 23 pp 1145– (1986)
[3] Fairweather, IMA J. Numer. Anal. 3 pp 173– (1983)
[4] Hlava’cek, Appl. Mat. 17 pp 327– (1972)
[5] Joubert, Numer. Math. 17 pp 409– (1971)
[6] ’A fully Galerkin method applied to parabolic problems’, Ph.D. Thesis, Montana State University, Bozeman Montana, 1987.
[7] Lund, Math. Comp. 47 pp 571– (1986)
[8] Seward, IMA J. Numer. Anal. 4 pp 375– (1984)
[9] Stenger, Math. Comp. 33 pp 85– (1979)
[10] Yu, Int. j. numer. methods eng. 23 pp 737– (1986)
[11] Circulant Matrices, Wiley, New York, 1979. · Zbl 0418.15017
[12] and , ’Symmetrization of the Sinc-Galerkin method with block techniques for elliptic equations’, submitted to IMA J. Numer. Anal. (1986).
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