Developing an iterative method to solve two- and three-dimensional mixed Volterra-Fredholm integral equations

Authors

  • Jafar Khazaeian Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
  • Noradin Parandin Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
  • Farajollah Yaghobi Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
  • Nasrin Karamikabir Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.

Keywords:

Nonlinear mixed Volterra-Fredholm integral equations, Iterative method, Banach xed point theorem, Numerical solution.

Abstract

An iterative method is extended to solve nonlinear two-
and three-dimensional mixed Volterra-Fredholm integral equations. We
consider the nonlinear operator form of these integral equations and
then develop the iterative method of Daftardar-Gejji and Jafari [3] to
solve them. Convergence property of the suggested schemes are proved
under some mild assumptions. In both cases, some numerical examples
are given to compare the performance of the proposed method with the
existing methods.

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Published

2021-05-25

Issue

Vol. 16

Section

Vol. 16, No. 2, (2022)

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