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The Multistage Optimal Homotopy Asymptotic Method for Nonlinear Weakly Singular Volterra Integral Equations |
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PP: 1-9 |
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Author(s) |
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Jafar Biazar,
Roya Montazeri,
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Abstract |
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| This paper is aimed to find an approximate solution to a weakly singular Volterra integral equation of the second kind, by
applying a new approach called multistage optimal homotopy asymptotic method (MOHAM). MOHAM is just a clear alteration of
the standard optimal homotopy asymptotic method (OHAM), in which in order to find a more accurate approximate solution, OHAM
will be applied in a consecutive sequence of subintervals. This approach is introduced for the first time by N. Ratib Anakira et al. in
2016 to approximate the solutions of differential equations with initial-values. Three examples are provided to demonstrate the validity
and reliability of the proposed approach. Numerical results reveal that the multistage procedure is a suitable tool for solving weakly
singular Volterra integral equations, where the domain of interest is not short enough. |
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