A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel ‎Method

الموضوعات : مجله بین المللی ریاضیات صنعتی

R. Ketabchi‎ ¹ , R. Mokhtari ² , E. Babolian ³

1 - Department of Mathematics, Science and Research branch, Islamic Azad University,Tehran,Iran.
2 - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran.
3 - Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.

تاريخ الإرسال : 18 الجمعة , صفر, 1438 تاريخ التأكيد : 18 الجمعة , صفر, 1438 تاريخ الإصدار : 12 الأربعاء , صفر, 1439

الکلمات المفتاحية: Reproducing kernel method, Volterra integral equations, Gram-Schmidt orthogonalization,

ملخص المقالة :

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The convergence analysis is established theoretically. The applicability of the iterative method is demonstrated by testing some various ‎examples.