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Several effective algorithms for nonlinear time fractional models

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  • Qin, Hongyu
  • Wu, Fengyan

Abstract

In this paper, several effective algorithms are proposed to simulate the time fractional models. A complete analysis of the algorithms for nonlinear problems is presented, while the previous investigations mainly focus on construction and analysis of L1-type method for the linear time fractional problems. After that, by using the sum-of-exponentials approximation, we develop the corresponding accelerated methods. We obtain that computational cost is reduced from O(N2) to O(logN) or O(log2N), where N denotes total number of time steps. Finally, several numerical experiments on several real-world models are proposed to confirm the effectiveness of the algorithms.

Suggested Citation

  • Qin, Hongyu & Wu, Fengyan, 2019. "Several effective algorithms for nonlinear time fractional models," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:36
    DOI: 10.1016/j.amc.2019.124598
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    References listed on IDEAS

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    1. Cheng, Xiujun & Duan, Jinqiao & Li, Dongfang, 2019. "A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 452-464.
    2. Zhang, Qifeng & Ren, Yunzhu & Lin, Xiaoman & Xu, Yinghong, 2019. "Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 91-110.
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