A new efﬁcient multi-parametric homotopy approach for two-dimensional Fredholm integral equations of the second kind

In this paper, a new multi-parametric homotopy approach is proposed to ﬁnd the approximate solution of linear and non-linear two-dimensional Fredholm integral equations of the second kind. In this framework, convergence of the proposed approach for these types of equations is investigated. This homo- topy contain two auxiliary parameters that provide a simple way of controlling the convergence region of series solution. The results of present method are compared with Adomian decomposition method (ADM) results which provide conﬁrmation for the validity of proposed approach. Two examples are presented to illustrate the accuracy and effectiveness of the proposed approach. 2000 AMS Classiﬁ cation: 45B05

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