Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation

• Published in: Applied mathematics and computation Vol. 271; pp. 11 - 21
• Main Authors: Bahşı, M. Mustafa, Çevik, Mehmet, Sezer, Mehmet
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.11.2015
• Subjects: Delay differential equation; Matrix method; Orthogonal exponential polynomials; Residual error technique; Orthogonal exponential polynomials; Matrix method; Residual error technique; Delay differential equation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2015.08.101

In this paper, a new matrix method based on orthogonal exponential (orthoexponential) polynomials and collocation points is proposed to solve the high-order linear delay differential equations with linear functional arguments under the mixed conditions. The convenience is that orthoexponential polynomials have shown to be effective in approximating a given function, fast and efficiently. An error analysis technique based on residual function is developed and applied to four problems to demonstrate the validity and applicability of the proposed method. It is confirmed that the present method yields quite acceptable results and the accuracy of the solution can significantly be increased by error correction and residual function.