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Mathematics of Computation

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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