Zayıf Tekil Çekirdekli Lineer İntegro Diferansiyel Denklemlerin Bir Sınıfının Chebyshev Seri Çözümleri

Year 2019, Volume: 9 Issue: 2, 314 - 328, 30.12.2019

Yalçın Öztürk

https://doi.org/10.37094/adyujsci.508986

Abstract

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. 

Keywords

İntegro-diferansiyel denklemlerin singular sistemleri, Zayıf tekil çekirdek, Abel denklemi, Sıralama metodu, Chebyshev polinomları

Chebyshev Series Solutions for a Class of System of Linear Integro-Differential Equations with Weakly Singular Kernel

Abstract

  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.

Keywords

Singular system of integro-differential equations, weakly singular kernel, Chebyshev polynomials, Abel's equation, Collocation method, Chebyshev polynomials

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