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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.