The Bivariate Shifted Legendre Functions for Nonlinear Volterra Integral Equation رسالة ماجستير

Abstract

In this thesis, the Bivariate Shifted Legendre Method for solving one, two and threedimensional nonlinear Volterra Integral Equation are introduced and analyzed. More speci c, three-dimensional Bivariate Shifted Legendre has been investigated in details and some formulas related to three-dimensional Volterra integral equation are deduced. Further, in order to nd the approximated solution, the Volterra integral Equation of the rst kind is converted to a second kind by using Leibniz integral formula and then the obtained integral equation is reduced to a system of linear algebraic equations using the bivariate shifted Legendre functions operational matrices. Finally, many numerical examples were provided to demonstrate the applicability and the accuracy of the presented method.