Residual correction of the Hermite polynomial solutions of the generalized pantograph equations

• Main Authors: Şuayip Yüzbaşı, Emrah GÖK, Mehmet SEZER
• Format: Article
• Language: English
• Published: BİSKA Bilisim Company 2015-02-01
• Series: New Trends in Mathematical Sciences
• Subjects: Pantograph equations; Hermite polynomials; collocation method; residual function.
• Online Access: https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=67
• ISSN: 2147-5520; 2147-5520

In this paper, we consider the residual correction of the Hermite polynomial solutions of the generalized pantograph equations. The Hermite polynomial solutions are obtained by a collocation method. By means of this collocation method, the problem is into a system of algebraic equations and thus unknown coefficients are determined. An error problem is constructed by using the orginal problem and the residual function. Error problem is solved by the Hermite collocation method and thus the imroved approximate solutions are gained. The technique is illustrated by studying the problem for two examples. The obtained results show that the residual corrcetion method is very effective.