A numerical approach with residual error estimation for solution of high-order linear differential-difference equations by using Gegenbauer polynomials
Also, by using the Mean-Value Theorem and residual function, an efficient error estimationtechnique is proposed and some illustrative examples are presented to demonstrate the validity and applicabilityof the method.
📌 3 Key Takeaways
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Objective & Hypothesis:The main aim of this study is to apply the Gegenbauer polynomials for the solution of high-order lineardifferential difference equations with functional arguments under initial-boundary conditions.The technique wehave used is essentially based on the truncated Gegenbauer series and its matrix representations along withcollocation points.
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Key Findings & Data:The main aim of this study is to apply the Gegenbauer polynomials for the solution of high-order lineardifferential difference equations with functional arguments under initial-boundary conditions.The technique wehave used is essentially based on the truncated Gegenbauer series and its matrix representations along withcollocation points.
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Conclusion & Impact:Also, by using the Mean-Value Theorem and residual function, an efficient error estimationtechnique is proposed and some illustrative examples are presented to demonstrate the validity and applicabilityof the method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
The main aim of this study is to apply the Gegenbauer polynomials for the solution of high-order lineardifferential difference equations with functional arguments under initial-boundary conditions.The technique wehave used is essentially based on the truncated Gegenbauer series and its matrix representations along withcollocation points. Also, by using the Mean-Value Theorem and residual function, an efficient error estimationtechnique is proposed and some illustrative examples are presented to demonstrate the validity and applicabilityof the method.
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Cite This Article
SEZER, M., MOLLAOĞLU, T. (2022). A numerical approach with residual error estimation for solution of high-order linear differential-difference equations by using Gegenbauer polynomials. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 13 - Sayı: 1, 39–49. https://ajindex.com/articles/472371
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