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Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 8، دوره 6، شماره 1، فروردین 2018، صفحه 80-97 اصل مقاله (167.76 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Farshid Mirzaee* 1؛ Nasrin Samadyar2 | ||
| 1Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 65719-95863, Malayer, Iran | ||
| 2Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran | ||
| چکیده | ||
| 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 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, accuracy of this scheme is checked with two numerical examples. The obtained results reveal efficiency and capability of the proposed method. | ||
| کلیدواژهها | ||
| Stochastic integrals؛ Operational matrix of integration؛ Wavelet؛ Legendre polynomials؛ Error analysis | ||
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