Computational Methods for Differential Equations Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations

Farshid Mirzaee, Nasrin Samadyar
2018 unpublished
In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to the nonlin-ear system of algebraic equations which can be solved by using a suitable numerical method
more » ... such as Newton's method. Convergence analysis with error estimate are given with full discussion. Also, we provide an upper error bound under weak assumptions. Finally, accuracy of this scheme is checked with two numerical examples. The obtained results reveal efficiency and capability of the proposed method.
fatcat:xc3plimjabfcjixpvhtqhrwje4