Open AccessLegendre-Galerkin method for the nonlinear Volterra-Fredholm integro-differential equations
Author(s) -
Mohamed Fathy
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2128/1/012036
Subject(s) - legendre polynomials , galerkin method , mathematics , convergence (economics) , nonlinear system , mathematical analysis , numerical analysis , differential equation , physics , quantum mechanics , economics , economic growth
The study of solving nonlinear integro-differential equations in Volterra-Fredholm type presents in this paper. The proposed method tends to use Legendre polynomials as a basis in the Galekin method to obtain the numerical solution. We use the Newton method to get the numerical solution of the nonlinear equations resulted from applying the Galerkin method. The comparison of the present study with the existing results in the literature shows an excellent agreement. Numerical examples explain the convergence, applicability, and efficiency of algorithm.