Abstract
In this paper, the existence of a unique solution of the nonlinear quadratic integral equation (NQIE) of the second kind with continuous kernels, under certain conditions, is considered. Then, Adomian Decomposition Method (ADM) and new modifications have been considered to obtain a nonlinear algebraic system (NAS), where the existence of a unique solution of this method is also, proved. Finally, numerical results are computed when the continuous kernels take some different forms. Moreover, the rate of convergence error, in each case, is computed.
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