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Numerical Algorithms

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15-07-2019 | Original Paper

Chebyshev-Legendre spectral method and inverse problem analysis for the space fractional Benjamin-Bona-Mahony equation

Authors: Hui Zhang, Xiaoyun Jiang, Rumeng Zheng

Published in: Numerical Algorithms | Issue 2/2020

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Abstract

In the paper, a space fractional Benjamin-Bona-Mahony (BBM) equation is proposed. For the direct problem, we develop the Chebyshev-Legendre spectral scheme for the proposed equation. The given approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the presented method, the computational complexity is reduced and both accuracy and efficiency are achieved compared with the Legendre spectral method. Stability and convergence analysis of the numerical method are proven. For the inverse problem, the Bayesian method is developed to estimate some relevant parameters based on the spectral format of the direct problem. The convergence analysis on the Kullback-Leibler distance between the true posterior distribution and the approximation is derived. Some numerical experiments are included to demonstrate the theoretical analysis.

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Title: Chebyshev-Legendre spectral method and inverse problem analysis for the space fractional Benjamin-Bona-Mahony equation
Authors: Hui Zhang
Xiaoyun Jiang
Rumeng Zheng
Publication date: 15-07-2019
Publisher: Springer US
Published in: Numerical Algorithms / Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00767-x

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