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Numerical solutions of integral and integro-differential equations using Legendre polynomials |
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| Authors: | A. H. Khater A. B. Shamardan D. K. Callebaut M. R. A. Sakran |
| Affiliation: | (1) Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;(2) Department of Mathematics, Faculty of Science, El-Minia University, El-Minia, Egypt;(3) Department of Physics, CGB, University of Antwerp, 2020 Antwerp, Belgium;(4) Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt |
| Abstract: | In this paper, a finite Legendre expansion is developed to solve singularly perturbed integral equations, first order integro-differential equations of Volterra type arising in fluid dynamics and Volterra delay integro-differential equations. The error analysis is derived. Numerical results and comparisons with other methods in literature are considered. |
| Keywords: | Volterra integral equations Singularly perturbed Volterra integral equations Boundary layer Integral equations of the convolution type Integro differential equations in fluid dynamics Delay integro differential equations Error analysis |
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