Solving system of Volterra integral equations of the first kind by modified Adomian decomposition method
Keywords:
Volterra integral equation, Adomian decomposition method, Semi-analytical solutionAbstract
In this work, we consider system of linear and nonlinear Volterra integral equations (VIEs) of the first kind. At first, we have converted system of VIEs of the first kind to an equation of the second kind by differentiation of transformation. Then standard Adomian decomposition method (ADM) and modified ADM (MADM) are used to find semi-analytical solution. The Adomian decomposition method converts Volterra integral equations of the second kind into determination of computable components of iterative integral equations. The uniqueness solutions of the system of nonlinear VIEs of the second kind are proved and the choice of the initial data is shown. It is practically shown that the obtained series by MADM convergence very rapidly to the exact solution. Finally, four examples were illustrated to show validity and applicability of this approach. The examples are taken from the works mentioned in the references.
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