Open AccessNonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions
Author(s) -
A. M. AlBugami
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021602
Subject(s) - adomian decomposition method , mathematics , fredholm integral equation , homotopy analysis method , nonlinear system , kernel (algebra) , fredholm theory , mathematical analysis , integro differential equation , integral equation , work (physics) , differential equation , homotopy , numerical analysis , pure mathematics , first order partial differential equation , physics , quantum mechanics , thermodynamics
This paper proposes a new definition of the nonlinear Fredholm integro-differential equation of the second kind with continuous kernel in two-dimensional (NT-DFIDE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions of NT-DFIDE are obtained by two powerful methods Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM). The given numerical examples showed the efficiency and accuracy of the introduced methods.