A Method for Numerical Solution of Third-Kind Volterra Integral Equations Using Krall-Laguerre Polynomials
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
P. Jami
1
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
E. Hashemizadeh
2
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
کلید واژه: Krall-Laguerre Polynomials, Approximation, Krall-Hahn Orthogonal Polynomials, Third-Kind Integral Equations, Analytical solution. Fredholm Integral Equations,
چکیده مقاله :
The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method.
حل عددی معادلات انتگرالی خطی از نوع سوم در مطالعات مختلف مورد بحث قرار گرفته است، اما در تحقیقات قبلی در مورد این نوع معادلات تنها راه حل تحلیلی بررسی شده است. با توجه به برخی محدودیت ها برای این نوع راه حل ها، در این مقاله روش جدیدی برای حل عددی معادلات انتگرالی خطی از نوع سوم پیشنهاد شده است. روش پیشنهادی براساس تقریب تابع مجهول با چند جمله ای کرال-لاگر است. این روش یک روش محاسباتی ساده با یک راه حل تقریبی کاملاً قابل قبول دارد. علاوه بر این، ما برآورد خطا برای روش پیشنهادی را بهدست می آوریم. دو مثال نیز برای نشان دادن موثربودن روش پیشنهادی ارائه شده است.
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