Solving Fuzzy Integral Equations of the Second Kind by using the Reproducing Kernel Hilbert Space Method

الموضوعات :

صدیقه فرزانه جوان ¹ (گروه ریاضی، دانشکده علوم پایه، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران)
سعید عباسبندی ² (گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه بین المللی امام خمینی (ره)، قزوین، ایران)
محمدعلی فریبرزی عراقی ³ (گروه ریاضی، دانشکده علوم پایه، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران)

تاريخ الإرسال : 24 الخميس , رجب, 1441 تاريخ التأكيد : 05 الإثنين , محرم, 1442 تاريخ الإصدار : 23 الأربعاء , ذو القعدة, 1443

الکلمات المفتاحية: Fuzzy numbers, Gram-Schmidt process, Reproducing Kernel Hilbert Space, Fuzzy integral equations,

ملخص المقالة :

In this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equation is converted to a system of crisp integral equations. Then, this system is solved by using the reproducing kernel method free of the Gram-Schmidt orthogonalization process. Also, two numerical algorithms are proposed based on applying the Gram-Schmidt process and without using it. The general form of numerical solution accordingly the reproducing kernel method is introduced and the convergence theorem of solution of the proposed scheme to the exact solution is proved. Finally, a sample fuzzy integral equation is solved by means of both suggested algorithms and the results are compared for differents points and levels. Due to the difficulties in applying the Gram-Schmidt process, the obtained results of the new algorithm are satisfactory.

المصادر:

 

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