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

نویسندگان
Gachpazan, M. ID 1
Beiglo, H. ID 2
Erfanian, M. ID 3

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

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

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

doi
10.22067/ijnao.v4i2.34304
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