In this paper, the Taylor expansion approach is developed for initial value problems for nonlinear integro-differential equations. This method transformed nonlinear integro-differential equation to a matrix equation which corresponds to a system of nonlinear equations with unknown coefficients. Results of approximate solution to test problems are demonstrated.
Mathematics Subject Classifications: 45J05; 47G20
A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations. In this paper, we obtain existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of Volterra-Fredholm integral equations.
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