Numerical Solution of Volterra-Fredholm Integral Equations with the Help of Inverse and Direct Discrete Fuzzy Transforms and Collocation Technique

در اين مقاله ، يك رهيافت جديد براي حل عددي معادلات انتگرالي ولترا-فردهلم با استفاده از روش بسط مبتني بر ادغام تبديلات فازي مستقيم و معكوس در تركيب با روش هم محلي ارايه مي شود . اولا ، تابع مجهول با استفاده از تركيب تبديلات فازي مستقيم و معكوس بر مبناي افراز فازي تقريب زده شده و سپس معادله ولترا- فردهلم به يك دستگاه معادلات خطي منجر ميشود . به علاوه ، قضيه همگرايي براي روش پيشنهاد شده با توجه به مدول پيوستگي آورده مي شود . درآخر مثالهايي جهت نشان دادن دقت و كارايي روش پيشنهاد شده ارايه مي شود .

In this paper, a new approach to the numerical solution of Volterra- Fredholm integral equations by using expansion method based on the composition of the inverse and direct discrete fuzzy transforms (shortly F-transforms) in combination with the collocation technique is proposed. First, the unknown function is approximated by using the composition of the inverse and direct discrete F-transforms based on the fuzzy partition, then the Volterra- Fredholm integral equation is reduced to the linear system of equations. Moreover, the convergence theorem for the proposed method is given in terms of the modulus of continuity. Finally, illustrative examples are included to show the accuracy and the efficiency of the proposed method.