Superconvergence results of iterated projection methods for linear Volterra integral equations of second kind |
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Authors: | Moumita Mandal Gnaneshwar Nelakanti |
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Affiliation: | 1.Department of Mathematics,Indian Institute of Technology Kharagpur,Kharagpur,India |
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Abstract: | In this paper, we develop the iteration techniques for Galerkin and collocation methods for linear Volterra integral equations of the second kind with a smooth kernel, using piecewise constant functions. We prove that the convergence rates for every step of iteration improve by order ({mathcal {O}}(h^{2})) for Galerkin method, whereas in collocation method, it is improved by ({mathcal {O}}(h)) in infinity norm. We also show that the system to be inverted remains same for every iteration as in the original projection methods. We illustrate our results by numerical examples. |
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