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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 3

New collocation scheme for solving fractional partial differential equations

Afshan KANWAL
Chang PHANG
Jian Rong LOH
Pages
1107–1125
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Some examples are given to illustrate the effectiveness and applicability of the proposed technique.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article concerned about the numerical solution of time fractional partial differential equations (FPDEs).
📊
Key Findings & Data:The proposed technique is using shifted Chebyshev-Gauss-Lobatto (CGL) collocation points in conjunction with an operational matrix of Caputo sense derivatives via Genocchi polynomials.
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Conclusion & Impact:Some examples are given to illustrate the effectiveness and applicability of the proposed technique.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Collocation method · shifted Chebyshev Gauss Lobatto · fractional partial differential equations

Abstract

This article concerned about the numerical solution of time fractional partial differential equations (FPDEs). The proposed technique is using shifted Chebyshev-Gauss-Lobatto (CGL) collocation points in conjunction with an operational matrix of Caputo sense derivatives via Genocchi polynomials. The system of linear algebraic equations is obtained when the main equation along with the initial as well as boundary conditions is collocated by using shifted CGL collocation points. The main approach to this method is to transform the FPDEs to system of algebraic equations, hence, greatly simplify the numerical scheme. Comparison of the obtained results with the existing methods depicts that the suggested method is highly effect, more efficient and have less computational work. Some examples are given to illustrate the effectiveness and applicability of the proposed technique.

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Cite This Article

KANWAL, A., PHANG, C., LOH, J. R. (2022). New collocation scheme for solving fractional partial differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 3, 1107–1125. https://ajindex.com/articles/529596

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