A Galerkin-Like Approach to Solve Multi-Pantograph Type Delay Differential Equations
FILOMAT, vol.32, no.2, pp.409-422, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 32 Issue: 2
- Publication Date: 2018
- Doi Number: 10.2298/fil1802409y
- Journal Name: FILOMAT
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.409-422
- Keywords: Delay differential equations, pantograph equation, Galerkin method, residual error correction, APPROXIMATION, ORDER, MODEL
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
In this paper, a Galerkin-like approach is presented to numerically solve multi-pantograph type delay differential equations. The method includes taking inner product of a set of monomials with a vector obtained from the equation under consideration. The resulting linear system is then solved, yielding a polynomial as the approximate solution. We also provide an error analysis and discuss the technique of residual correction, which aims to increase the accuracy of the approximate solution. Lastly, the method, error analysis and the residual correction technique are illustrated with several examples. The results are also compared with numerous existing methods from the literature.