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Farshid Mirzaee

Farshid Mirzaee

Academic rank: Professor
ORCID: 0000-0002-1429-2548
Education: PhD.
ScopusId: 6508385954
HIndex: 34/00
Faculty: Mathematical Sciences and Statistics
Address: Faculty of Mathematical Sciences and Statistics, Department of Applied Mathematics, Malayer University, 4 Km Malayer-Arak Road, P. O. Box 65719-95863, Malayer, Iran.
Phone: +98 - 81 - 32457459

Research

Title
Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations
Type
JournalPaper
Keywords
Stochastic integrals; Operational matrix of integration ; Wavelet; Legendre polynomials; Error analysis.
Year
2018
Journal computational methods for differential equations
DOI
Researchers Farshid Mirzaee

Abstract

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 prop- erty 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 suit- able 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.