SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS
نویسندگان
چکیده مقاله:
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 transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether 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 themethod.
منابع مشابه
solving nonlinear two-dimensional volterra integral equations of the first-kind using bivariate shifted legendre functions
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 transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...
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عنوان ژورنال
دوره 5 شماره 3 (SUMMER)
صفحات 219- 230
تاریخ انتشار 2015-03-21
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