SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 5، 3 (SUMMER)، فروردین 2015، صفحه 219-230   

نویسندگان

Somayeh Nemati؛ Y. Ordokhani

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

چکیده

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformed
to a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties of
the bivariate shifted Legendre functions are presented. The operational matrices of integration
together with the product operational matrix are utilized to reduce the solution of the second-kind equation to the solution of a system of linear algebraic equations. Finally, a system of nonlinear algebraic equations is obtained to give an approximate solution of the main problem.
Also, numerical examples are included to demonstrate the validity and applicability of the
method.