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 |