SOLVING INTEGRAL EQUATIONS WITH LOGARITHMIC KERNEL BY USING PERIODIC QUASI-WAVELET

In solving integral equations with logarithmic kernel which arises from the boundary integral equation reformulation of some boundary value problems for the two dimensional Helmholtz equation, we combine the Galerkin method with Beylkin's ([2]) approach, series of dense and nonsymmetric matrice...

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Bibliographic Details
Published in:Journal of computational mathematics 2000-09, Vol.18 (5), p.487-512
Main Authors: Chen, Han-lin, Peng, Si-long
Format: Article
Language:English
Subjects:
Approximation
Computational mathematics
Differential equations
Error analysis
Galerkin methods
Integers
Linear systems
Matrices
Polynomials
Spline functions
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Summary:In solving integral equations with logarithmic kernel which arises from the boundary integral equation reformulation of some boundary value problems for the two dimensional Helmholtz equation, we combine the Galerkin method with Beylkin's ([2]) approach, series of dense and nonsymmetric matrices may appear if we use traditional method. By appealing the so-called periodic quasi-wavelet (PQW in abbr.) ([5]), some of these matrices become diagonal, therefore we can find a algorithm with only O(K(m)²) arithmetic operations where m is the highest level. The Galerkin approximation has a polynomial rate of convergence.
ISSN:0254-9409
1991-7139