10.30495/fomj.2022.1950726.1058

Solving linear and nonlinear Volterra Fuzzy Integral Equations System via Differential Transform Method

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  • Mahmoud Paripour*1,
  • Mandana Takrimi2,
  1. Hamedan University Of Technology, Hamedan, 65169-13418, Iran.
  2. Sama Technical and Vocational Training College, Islamic Azad University, Dezful Branch, Dezful, Iran.

Received: 2022-01-25

Accepted: 2022-08-09

Published in Issue 2022-07-01

Copyright (c) 2024 Fuzzy Optimization and Modeling Journal

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How to Cite

Paripour, M., & Takrimi, M. (2022). Solving linear and nonlinear Volterra Fuzzy Integral Equations System via Differential Transform Method. Fuzzy Optimization and Modeling Journal (FOMJ), 3(3), 19-32. https://doi.org/10.30495/fomj.2022.1950726.1058
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Abstract

In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral equations system into two crisp integral equations systems of Volterra; then we solve each of them via DTM. If the equation has a solution in terms of the series expansion of known functions; this powerful method will catch the exact solution. Moreover, the ability and efficiency of the algorithm are shown by solving some numerical examples.In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral equations system into two crisp integral equations systems of Volterra; then we solve each of them via DTM. If the equation has a solution in terms of the series expansion of known functions; this powerful method will catch the exact solution. Moreover, the ability and efficiency of the algorithm are shown by solving some numerical examples.

Keywords

  • Fuzzy Integral Equations,
  • Volterra Integral,
  • Differential Transform Method,
  • Error estimation
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