On the numerical solution of singular integro-differential equations

Authors:
N. I. Ioakimidis and P. S. Theocaris

Journal:
Quart. Appl. Math. **37** (1979), 325-331

MSC:
Primary 65R20

DOI:
https://doi.org/10.1090/qam/548991

MathSciNet review:
548991

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Abstract: A method of numerical solution of a sufficiently wide class of Cauchy-type singular integrodifferential equations along a straight finite interval is presented. This method consists of approximating the integrals in such an equation by using appropriate numerical integration rules and appropriately-selected collocation points and reducing such an equation to a system of linear algebraic equations. This technique constitutes a direct generalization of the corresponding methods of numerical solution of Cauchy-type singular integral equations and presents some advantages over the classical Multhopp method of numerical solution of Cauchy-type singular integrodifferential equations, to which it reduces in some special cases. An application to a specific equation is also made.

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DOI:
https://doi.org/10.1090/qam/548991

Article copyright:
© Copyright 1979
American Mathematical Society