Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity

The main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-12, Vol.13 (12), p.2370
Main Authors: Izadi, Mohammad, Yüzbaşı, Şuayip, Ansari, Khursheed J.
Format: Article
Language:English
Subjects:
Approximation
collocation method
Collocation methods
Control theory
Differential equations
error analysis
Mathematical analysis
multi-pantograph delay differential equations
Pantographs
Polynomials
Quantum dots
Singularities
singularity
Vieta–Lucas functions
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Summary:The main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the aforementioned differential equations. Moreover, an error bound of the present approach by using the maximum norm was computed and an error estimation technique based on the residual function is presented. Finally, the validity and applicability of the presented collocation scheme are shown via four numerical test examples.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13122370