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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 8 > No. 1


The Multistage Optimal Homotopy Asymptotic Method for Nonlinear Weakly Singular Volterra Integral Equations

PP: 1-9
Jafar Biazar, Roya Montazeri,
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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