A spline collocation method for parabolic pseudodifferential equations
type: Item
instance of: scholarly article
title: A spline collocation method for parabolic pseudodifferential equations
zbMATH Open document ID: 1013.65109
DOI: 10.1016/S0377-0427(01)00401-0
author: Juha Anttila
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: A boundary element collocation method for some parabolic pseudodifferential equations is examined. The two-dimensional heat conduction problem with vanishing initial condition and a given Neumann or Dirichlet type boundary condition is chosen as the basic model. The parabolic pseudodifferential operators are contained in the boundary integral equations of the first kind (being the single layer and the hypersingular heat operator equations). The collocation schema is reduced to an equivalent Galerkin type problem. For the approximation of the solution tensor products of spline functions are used. The spatial variable is approximated by periodic smoothest splines of arbitrary high odd degree and the time variable is approximated by piecewise linear continuous splines. Stability and convergence of the method are proved with respect to some anisotropic Sobolev norms. Some results of this paper are more general than those obtained by \textit{M. Costabel} and \textit{J. Saranen} [Numer. Math. 84, No.~3, 417-449 (2000; Zbl 0967.65103)].
reviewed by: Nikolai Pleshchinskii
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35S10
zbMATH DE Number: 1758419
zbMATH Keywords: collocation method
zbMATH Keywords: boundary integral equation
zbMATH Keywords: parabolic pseudodifferential equation
zbMATH Keywords: Galerkin method
zbMATH Keywords: heat conduction problem
zbMATH Keywords: spline function
zbMATH Keywords: stability
zbMATH Keywords: convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1758419