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Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations. (English) Zbl 1438.65335

Summary: 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 the orthogonality property and therefore the coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method 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, the accuracy of this scheme is checked with two numerical examples. The obtained results reveal efficiency and capability of the proposed method.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
60H05 Stochastic integrals
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65T60 Numerical methods for wavelets
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