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

Fuzzy Optimization and Modeling Journal

مقاله 2، دوره 3، شماره 3، مهر 2022، صفحه 19-32   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/fomj.2022.1950726.1058

نویسندگان

Mahmoud Paripour^{* 1}؛ Mandana Takrimi²

¹Hamedan University Of Technology, Hamedan, 65169-13418, Iran.

²Sama Technical and Vocational Training College, Islamic Azad University, Dezful Branch, Dezful, Iran.

چکیده

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.

کلیدواژه‌ها

Fuzzy Integral Equations System؛ Volterra Integral؛ Differential Transform Method؛ Error estimation