New iterative method for solving linear Fredholm fuzzy integral equations of the second kind

معادلات انتگرال فازي نقش مهمي در علوم مختلفي دارند لذا در اين مقاله يك روش جديد براي يافتن تقريبي از جواب معادلات انتگرال فازي ارايه مي شود. در اين روش با استفاده از بسط تيلور معادله انتگرال فازي به يك دستگاه معادله خطي تبديل مي شود. براي اين منظور به جاي تابع مجهول سري تيلور جا گذاري مي شود سپس از دو سود معادله انتگرال N بار مشتق گرفته مي شود و جواب معادله انتگرال از حل دستگاه معادله خطي حاصل به دست مي آيد. كارايي اين روش با چند مثال عددي بررسي خواهد شد.

Fuzzy integral equations play major roles in various areas, therefore a new method for finding a solution of the Fredholm fuzzy integral equation is presented. This method converts the fuzzy integral equation into linear system by using the Taylor series. For this scope, first the Taylor expansion of unknown function is substituted in parametric form of the given equation. Then we differentiate both sides of the resulting integral equation and also approximate the Taylor expansion by a suitable truncation limit. This work yields a linear system in crisp case. Now the solution of this system yields unknown Taylor coefficients of the solution functions. The proposed method is illustrated by several examples with computer simulations.