On solving weakly singular Volterra equations of the first kind with Galerkin approximations-Reference-Cited by-同舟云学术

On solving weakly singular Volterra equations of the first kind with Galerkin approximations

Published:1976 Issue:136 Volume:30 Page:747-757
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Bownds John M.

Abstract

The basic linear, Volterra integral equation of the first kind with a weakly singular kernel is solved via a Galerkin approximation. It is shown that the approximate solution is a sum with the first term being the solution of Abel’s equation and the remaining terms computable as components of the solution of an initial-value problem. The method represents a significant decrease in the normal number of computations required to solve the integral equation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1976-30-136/S0025-5718-1976-0438747-8/S0025-5718-1976-0438747-8.pdf

Reference15 articles.

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2. G. KOWALEWSKI, Integralgleichungen, de Gruyter, Berlin, 1930.

3. On the numerical solution of equations of the Abel type;Fettis, Henry E.;Math. Comp.,1964

4. A product integration method for a class of singular first kind Volterra equations;Weiss, R.;Numer. Math.,1971

5. On the numerical solution of Brownian motion processes;Anderssen, R. S.;J. Appl. Probability,1973

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