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Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation. (English) Zbl 1197.65232

Summary: A numerical method based on sinc collocation approximation for a class of nonlinear weakly singular Volterra integral equations of a second kind with non-smooth solution is given. The numerical method given here combines a sinc collocation method with an explicit iterative process that involves solving a system of nonlinear equations. We provide an error analysis for the method. It is shown that the approximate solution converges to the exact solution at the rate of \(\sqrt{M} \exp (-c\sqrt{M})\), where \(M\) is the number of collocation points and \(c\) is some positive constant. Some numerical results for several test functions are given to confirm the accuracy and the ease of implementation of the method.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G05 Singular nonlinear integral equations
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