A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials
Also, by using the Mean-Value Theorem and residual function, an efficient error estimation technique is proposed and some illustrative examples are presented to demonstrate the validity and applicability of 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 linear differential difference equations with functional arguments under initial-boundary conditions.The technique we have used is essentially based on the truncated Gegenbauer series and its matrix representations along with collocation 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 linear differential difference equations with functional arguments under initial-boundary conditions.The technique we have used is essentially based on the truncated Gegenbauer series and its matrix representations along with collocation points.
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Conclusion & Impact:Also, by using the Mean-Value Theorem and residual function, an efficient error estimation technique is proposed and some illustrative examples are presented to demonstrate the validity and applicability of the method.
The main aim of this study is to apply the Gegenbauer polynomials for the solution of high-order linear differential difference equations with functional arguments under initial-boundary conditions.The technique we have used is essentially based on the truncated Gegenbauer series and its matrix representations along with collocation points. Also, by using the Mean-Value Theorem and residual function, an efficient error estimation technique is proposed and some illustrative examples are presented to demonstrate the validity and applicability of the method.
Mollaoğlu, T., Sezer, M. (2017). A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 13 Sayı: 1, 39–49. https://doi.org/10.18466/cbayarfbe.302638