Discrete homotopy analysis method for the nonlinear Fredholm integral equations

Abstract Recently, Behiry et al. (in press) [8] have introduced a discretized version of the Adomian decomposition method, namely “Discrete Adomian Decomposition Method (DADM)”, for solving nonlinear Fredholm integral equations. In this paper, we extent Behiry et al.’s idea on the well-known homotopy analysis method, and introduce “Discrete homotopy analysis method (DHAM)”. The obtained numerical solutions by the present method are compared with the obtained results by DADM. Also, we present some advantages of DHAM which DADM has not them. Comparison of the DHAM with the DADM reveals that former is more powerful than the later and also DADM is only special case of the DHAM.

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