adyu j sci Adıyaman University Journal of Science 2147-1630 2146-586X Adıyaman University 10.37094/adyujsci.508986 Mathematical Sciences Applied Mathematics Matematik Uygulamalı Matematik Zayıf Tekil Çekirdekli Lineer İntegro Diferansiyel Denklemlerin Bir Sınıfının Chebyshev Seri Çözümleri Chebyshev Series Solutions for a Class of System of Linear Integro-Differential Equations with Weakly Singular Kernel Öztürk Yalçın MUĞLA SITKI KOÇMAN ÜNİVERSİTESİ 12 30 2019 9 2 314 328 01 06 2019 12 18 2019 Copyright © 2011, Adıyaman University Journal of Science 2011 Adıyaman University Journal of Science

Bu çalışmada, zayıf tekil çekirdekli lineer integro diferansiyel denklemlerin bir sınıfı için bir nümerik algoritma sunulacaktır. Bu algoritma birinci tip Chebyshev polinom bazı yardımıyla polinom yaklaşımı ve sıralama metodunu temel almaktadır. Bu metot verilen denklem ve koşulları bir matris denklemine dönüştürür. Nümerik metodun uygulanabilirliğini ve doğruluğunu göstermek amacıyla bazı örnekler incelenecektir. Sunulan metot diğer metotlar ile kıyaslanmıştır.

In this study, a numerical algorithm for solving a class of system of linear integro differential equations with weakly singular kernel is presented. This algorithm is based on polynomial approximation and collocation method, using the first kind Chebyshev polynomial basis. This method transforms the equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. To show the validity and applicability of the numerical method some experiments are examined. Present method is compared some numerical methods.

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