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Numerical solution of multi-Pantograph delay boundary value problems via an efficient approach with the convergence analysis

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Abstract

This present investigation is contemplated to provide Legendre spectral collocation method for solving multi-Pantograph delay boundary value problems (BVPs). In this regard, an equivalent integral form of such BVPs has been considered. The proposed method is based on Legendre–Gauss collocation nodes and Legendre–Gauss quadrature rule. Convergence analysis associated to the presented scheme has been provided to show its applicability theoretically. Some numerical examples are given to demonstrate the efficiency, accuracy, and versatility of our method. Numerical results confirm the theoretical predictions and are superior with respect to several recent numerical methods including Hermite collocation approach, Laguerre collocation technique and the reproducing kernel method.

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Acknowledgements

This work was supported by National Natural Science Foundation of China Project (11671342), Hunan Education Department Key Project (17A210, 16C0139), and Hunan Province Natural Science Fund (2018JJ2374). Also, the authors thank the Editor and the reviewers for their constructive comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yin Yang

  2. Department of Mathematics, Kosar University of Bojnord, P. O. Box 9415615458, Bojnord, Iran

    Emran Tohidi

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  1. Yin Yang
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  2. Emran Tohidi
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Correspondence to Emran Tohidi.

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Communicated by Jose Alberto Cuminato.

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Yang, Y., Tohidi, E. Numerical solution of multi-Pantograph delay boundary value problems via an efficient approach with the convergence analysis. Comp. Appl. Math. 38, 127 (2019). https://doi.org/10.1007/s40314-019-0896-3

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  • DOI: https://doi.org/10.1007/s40314-019-0896-3

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