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Solving nonlinear Volterra-Fredholm integro-differential equations using the modified Adomian decomposition method. (English) Zbl 1183.41019
Summary: A nonlinear Volterra-Fredholm integro-differential equation is solved by using the modified Adomian decomposition method (MADM). The approximate solution of this equation is calculated in the form of a series in which its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. The existence, uniqueness and convergence and an error bound of the proposed method are proved. Some examples are presented to illustrate the efficiency and the performance of the modified decomposition method.
MSC:
41A30Approximation by other special function classes
65L80Numerical methods for differential-algebraic equations