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A spectral order method for solving the nonlinear fourth-order time-fractional problem

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Abstract

In this paper, the nonlinear fourth-order time-fractional equation is considered by the combination of the Sinc-Galerkin method and the double exponential (DE) transformation. The backward Euler method is employed for the first order time derivative and the L1 formula is applied to the discretization of the Caputo time fractional derivative. For the spatial approximation, the DE Sinc-Galerkin method is employed. Using \(2N+1\) Sinc points, the convergence rate of the DE Sinc-Galerkin scheme is \(O(\exp (-CN/\log (N))\). Three numerical experiments are implemented to show the feasibility and high efficiency of the proposed scheme. Besides, the numerical results demonstrate that the Sinc-Galerkin scheme can achieve expected convergence order for the problems with singular points.

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Acknowledgements

This research was supported by the National Science Foundation of China (No. 12071127; No. 12171147 ), the Postgraduate Scientific Research Innovation Project of Hunan Province (No. CX20210469) and the Construct Program of the Key Discipline in Hunan (No. 19K056), Performance Computing and Stochastic Information Processing (Ministry of Education of China).

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Authors and Affiliations

  1. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education),School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Jing Guo, Qing Pan, Da Xu & Wenlin Qiu

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  1. Jing Guo
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  2. Qing Pan
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Correspondence to Jing Guo.

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Guo, J., Pan, Q., Xu, D. et al. A spectral order method for solving the nonlinear fourth-order time-fractional problem. J. Appl. Math. Comput. 68, 4645–4667 (2022). https://doi.org/10.1007/s12190-022-01719-w

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  • DOI: https://doi.org/10.1007/s12190-022-01719-w

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