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AIMS Mathematics

2021, Volume 6, Issue 10: 10383-10394. doi: 10.3934/math.2021602
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Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions

  • Department of Mathematics, Faculty of Sciences Taif University, Taif, Saudi Arabia
  • Received: 14 April 2021 Accepted: 08 July 2021 Published: 16 July 2021

  • MSC : 34A45, 65C40, 37N30

  • 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.

    Citation: A. M. Al-Bugami. Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions[J]. AIMS Mathematics, 2021, 6(10): 10383-10394. doi: 10.3934/math.2021602

    Related Papers:

  • 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.


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