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## A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials

#### Tuğçe Mollaoğlu [1] , Mehmet Sezer [2]

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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.

Gegenbauer polynomials, Differential- difference equations, Collocation method, Matrix method, Error estimation, Residual function
• M. T. Rashed, Numerical solution of functional differential,integral and integro- differential equations, Appl.Math.Comput.156 (2004) 485-492.
Subjects Engineering Articles Author: Tuğçe Mollaoğlu Author: Mehmet Sezer
 Bibtex @research article { cbayarfbe302638, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {Celal Bayar University}, year = {2017}, volume = {13}, pages = {39 - 49}, doi = {10.18466/cbayarfbe.302638}, title = {A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials}, key = {cite}, author = {Mollaoğlu, Tuğçe and Sezer, Mehmet} } APA 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 University Journal of Science, 13 (1), 39-49. DOI: 10.18466/cbayarfbe.302638 MLA Mollaoğlu, T , Sezer, M . "A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials". Celal Bayar University Journal of Science 13 (2017): 39-49 Chicago Mollaoğlu, T , Sezer, M . "A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials". Celal Bayar University Journal of Science 13 (2017): 39-49 RIS TY - JOUR T1 - A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials AU - Tuğçe Mollaoğlu , Mehmet Sezer Y1 - 2017 PY - 2017 N1 - doi: 10.18466/cbayarfbe.302638 DO - 10.18466/cbayarfbe.302638 T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 39 EP - 49 VL - 13 IS - 1 SN - 1305-130X-1305-1385 M3 - doi: 10.18466/cbayarfbe.302638 UR - https://doi.org/10.18466/cbayarfbe.302638 Y2 - 2019 ER - EndNote %0 Celal Bayar University Journal of Science A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials %A Tuğçe Mollaoğlu , Mehmet Sezer %T A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials %D 2017 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 13 %N 1 %R doi: 10.18466/cbayarfbe.302638 %U 10.18466/cbayarfbe.302638 ISNAD Mollaoğlu, Tuğçe , Sezer, Mehmet . "A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials". Celal Bayar University Journal of Science 13 / 1 (March 2017): 39-49. https://doi.org/10.18466/cbayarfbe.302638