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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2019 / Cilt: 9 - Sayı: 2

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

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

Yalçın ÖZTÜRK
Pages
314–328
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Present method is compared some numerical methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a numerical algorithm for solving a class of system of linear integro differential equations with weakly singular kernel is presented.
📊
Key Findings & Data:This algorithm is based on polynomial approximation and collocation method, using the first kind Chebyshev polynomial basis.
💡
Conclusion & Impact:Present method is compared some numerical methods.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

Özet

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.

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Cite This Article

ÖZTÜRK, Y. (2022). Chebyshev Series Solutions for a Class of System of Linear Integro-Differential Equations with Weakly Singular Kernel. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 - Sayı: 2, 314–328. https://ajindex.com/articles/428480

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