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

Author:
John M. Bownds

Journal:
Math. Comp. **30** (1976), 747-757

MSC:
Primary 65R05; Secondary 45E10

DOI:
https://doi.org/10.1090/S0025-5718-1976-0438747-8

Corrigendum:
Math. Comp. **31** (1977), 808.

Corrigendum:
Math. Comp. **31** (1977), 808.

MathSciNet review:
0438747

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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.

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0438747-8

Article copyright:
© Copyright 1976
American Mathematical Society