Modified nodal cubic spline collocation for biharmonic equations
type: Item
instance of: scholarly article
title: Modified nodal cubic spline collocation for biharmonic equations
zbMATH Open document ID: 1117.65158
author: Abeer Ali Abushama
author: B. Bialecki
published in: Numerical Algorithms
publication date: 2007-04-19T00:00:00Z
review text: The authors formulate a mixed approach with a modified cubic spline collocation scheme in order to solve the biharmonic Dirichlet problem on a rectangle. They prove the existence and the uniqueness of the solution and show how the scheme can be solved at a low cost. The scheme produces fourth order approximation for the solution, in the global maximum norm, and the same order for the partial derivatives of the solution in the partition nodes. Two test problems are solved in order to underline the qualities of the method.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 5145104
zbMATH Keywords: mixed formulation
zbMATH Keywords: nodal collocation
zbMATH Keywords: cubic splines
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: numerical examples
zbMATH Keywords: biharmonic Dirichlet problem
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s11075-007-9064-8
OpenAlex ID: W1966953392
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DOI: 10.1007/S11075-007-9064-8
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description: scientific article; zbMATH DE number 5145104