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A Legendre reproducing kernel method with higher convergence order for a class of singular two-point boundary value problems

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Abstract

We study a higher-order Legendre reproducing kernel method (LRKM) for singular two-point boundary value problems (BVPs). Our method relies upon Legendre polynomials. We carry out error estimatation by using interpolation theory. Various numerical tests including linear and nonlinear problems are performed to reveal the stability and efficiency of the new scheme. Therewith, as an application of the proposed approach, a famous time-dependent partial differential equation, namely Allen–Cahn test problem, is transfomed into the associated system of linear BVPs by localizing in temporal variable and is challenged numerically in details by the LRKM.

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Acknowledgements

The authors would like to express their thanks to unknown referee and also the handling editor for the careful reading of this research paper and helpful notes and comments.

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Authors and Affiliations

  1. College of Science, Zhejiang University of Technology, Hangzhou, 310023, China

    Minqiang Xu

  2. Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Emran Tohidi

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Emran Tohidi

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  1. Minqiang Xu
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  2. Emran Tohidi
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Correspondence to Emran Tohidi.

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Xu, M., Tohidi, E. A Legendre reproducing kernel method with higher convergence order for a class of singular two-point boundary value problems. J. Appl. Math. Comput. 67, 405–421 (2021). https://doi.org/10.1007/s12190-020-01494-6

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