Numerical approach for nonlinear system of Fredholm-Volterra integral equations
Z. K. Eshkuvatov)Faculty of Ocean Engineering Technology and Informatics (FOETI), University Malaysia Terengganu (UMT), Kuala Terengganu, MalaysiaHusnida Mamatova)Faculty of Applied Mathematics and Intellectual Technology, National University of Uzbekistan (NUUz), Tashkent, UzbekistanShahrina Ismail)Faculty of Science and Technology, University Sains Islam Malaysia (USIM), Negeri Sembilan, MalaysiaIlyani Abdullah)Faculty of Ocean Engineering Technology and Informatics (FOETI), University Malaysia Terengganu (UMT), Kuala Terengganu, MalaysiaRakhmatillo Aloev)Faculty of Applied Mathematics and Intellectual Technology, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan
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Abstract
In this note, the homotopy analysis method (HAM) is applied as a tool for solving the system of non-linear Fredholm-Volterra integral equations. The generalized chain rule is implemented for differentiation of the non-linear kernel functions with many variables, and the non-linear problem is reduced into a sequence of known non-linear integral equa- tions. The proposed method is compared with the homotopy perturbation method (HPM) given in Yusufogli [20] and Biazar and Ghazyini [21]. Numerical results reveal that the proposed method is very effective with high accuracy and dominated the HPM.
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