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Computing the singular behavior of solutions of Cauchy singular integral equations with variable coefficients

โœ Scribed by J. Li; R.P. Srivastav

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
319 KB
Volume
10
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

A numerical technique to determine the singular behavior of the solution of Cauchy singular integral equations (CSIE) with variable coefficients is proposed. The fundamental solution, which is a solution of the corresponding homogeneous equation, is constructed by a quadraturecollocation scheme. This leads to a system of nonlinear equations to approximate the exponents of singularity. Newton's method has been found to yield a useful approximation to these exponents. Once we have numerically obtained the weight function which determines the behavior of the solution of Cauchy singular integral equation, it can be used to solve a variety of nonhomogeneous CSIE with variable coefficients.

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