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Solving nonlinear Volterra integro-differential equation by using Legendre polynomial approximations. (English) Zbl 1325.65183

Summary: In this paper, we construct a new iterative method for solving a nonlinear Volterra integro-differential equation of the second kind, by approximating the Legendre polynomial basis. An error analysis is worked out using the Banach fixed point theorem. We compute the approximate solution without using a numerical method. Finally, some examples are given to compare the results with some of the existing methods.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
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