On the numerical solution of singular integro-differential equations
1979; Brown University; Volume: 37; Issue: 3 Linguagem: Inglês
10.1090/qam/548991
ISSN1552-4485
AutoresN. I. Ioakimidis, P. S. Theocaris,
Tópico(s)Iterative Methods for Nonlinear Equations
ResumoA 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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