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Product integration methods for solving a system of nonlinear Volterra integral equations |
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| Authors: | Bartur Jumarhon Sean McKee |
| Institution: | 1. School of Computing and Mathematical Sciences, Oxford Brookes University, Gipsy Lane Campus, Headington, Oxford OX3 0BP, United Kingdom;2. Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom |
| Abstract: | In this paper the technique of subtracting out singularities is used to derive explicit and implicit product Euler schemes with order one convergence and a product trapezoidal scheme with order two convergence for a system of Volterra integral equations with a weakly singular kernel. The convergence proofs of the numerical schemes are presented; these are nonstandard since the nonlinear function involved in the integral equation system does not satisfy a global Lipschitz condition. |
| Keywords: | Volterra equations Product integration methods |
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