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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

MSC:
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
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