Solving nonlinear Volterra integro-differential equation by using Legendre polynomial approximations

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 4، شماره 2 - شماره پیاپی 6، بهمن 2014، صفحه 73-83   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v4i2.34304

نویسندگان

M. Gachpazan^* ؛ M. Erfanian؛ H. Beiglo

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

چکیده

‎In this paper‎, ‎we construct a new iterative method for solving nonlinear Volterra Integral Equation of second kind‎, ‎by approximating the Legendre polynomial basis‎. ‎Error analysis is worked using Banach fixed point theorem‎. ‎We compute the approximate solution without using numerical method‎. ‎Finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

کلیدواژه‌ها

Nonlinear Volterra integro-differential equation؛ Legendre poly-nomial؛ Error analysis

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