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Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation


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1 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India
     

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In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

Keywords

Modied Adomian Decomposition Method, Fuzzy Volterra-Fredholm Integral Equations, Approximate Solution, Existence and Convergence Analysis.
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  • Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation

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Authors

Ahmed A. Hamoud
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India
Kirtiwant P. Ghadle
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India

Abstract


In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

Keywords


Modied Adomian Decomposition Method, Fuzzy Volterra-Fredholm Integral Equations, Approximate Solution, Existence and Convergence Analysis.

References