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Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem

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Abstract

In this paper, a linearized L1-Galerkin finite element method (FEM) is proposed to solve the nonlinear coupled time-fractional prey–predator problem. In order to derive the unconditionally optimal \(L^2\)-norm error estimate of the numerical scheme, the time-space error splitting technique is utilized in the convergence analysis. In addition, the unconditional superclose and superconvergence results under the bilinear finite element are deduced in details. To numerically solve the system with nonsmooth solutions and improve computational efficiency, we utilize nonuniform L1 scheme in time and construct the corresponding fast algorithm based on sum-of-exponentials technique. Finally, numerical examples are reported to show the accuracy of the proposed FEMs and the effectiveness of the fast algorithm.

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Acknowledgements

This work was supported by NSF of China (No. 11801527).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China

    Yu Lu & Meng Li

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  1. Yu Lu
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  2. Meng Li
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Correspondence to Meng Li.

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Lu, Y., Li, M. Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem. Comp. Appl. Math. 42, 111 (2023). https://doi.org/10.1007/s40314-023-02261-6

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