### IMPLICITY LINEAR COLLOCATION METHOD AND ITERATED IMPLICITY LINEAR COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN FREDHOLM INTEGRAL EQUATIONS ON 2D IRREGULAR DOMAINS

1. 1. Department of Mathematics, Farhangian University, Tehran, Iran;
• Received:2017-08-28 Revised:2018-10-04 Online:2020-07-15 Published:2020-07-15

H. Laeli Dastjerdi, M. Nili Ahmadabadi. IMPLICITY LINEAR COLLOCATION METHOD AND ITERATED IMPLICITY LINEAR COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN FREDHOLM INTEGRAL EQUATIONS ON 2D IRREGULAR DOMAINS[J]. Journal of Computational Mathematics, 2020, 38(4): 624-637.

In this work, we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs show to be the most promising RBFs for this kind of equations. The proposed methods are mesh-free and they are independent of the geometry of domain. Convergence analysis of the proposed methods together with some benchmark examples are provided which support their reliability and numerical stability.

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