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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Mandal, M., Nelakanti, G. Superconvergence results of iterated projection methods for linear Volterra integral equations of second kind. J. Appl. Math. Comput. 57, 321–332 (2018). https://doi.org/10.1007/s12190-017-1108-1
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DOI: https://doi.org/10.1007/s12190-017-1108-1
Keywords
- Volterra integral equations
- Smooth kernels
- Projection methods
- Piecewise polynomials
- superconvergence rates