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Numerical solution of fractional pantograph equations via Müntz–Legendre polynomials

In this paper, two new collocation methods to obtain a solution for fractional pantograph equations are developed. The primary one is a single-domain collocation scheme based on modified Müntz–Legendre polynomials which have high accuracy. The other one, modified shifted Müntz–Legendre polynomials a...

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Bibliographic Details
Published in:Mathematical sciences (Karaj, Iran) Iran), 2024-09, Vol.18 (3), p.387-395
Main Author: Tavassoli Kajani, M.
Format: Article
Language:English
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Summary:In this paper, two new collocation methods to obtain a solution for fractional pantograph equations are developed. The primary one is a single-domain collocation scheme based on modified Müntz–Legendre polynomials which have high accuracy. The other one, modified shifted Müntz–Legendre polynomials are applied to derive a multi-domain collocation scheme equipped with domain decomposition. The use of the shifted Müntz–Legendre polynomials and the domain decomposition leads to an appropriate approximate solution with few collocation points. We illustrate the accuracy and efficiency of these methods with a few numerical examples.
ISSN:2008-1359
2251-7456
DOI:10.1007/s40096-022-00507-8