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Spectral deferred correction method for fractional initial value problem with Caputo–Hadamard derivative

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  • Liu, Xiaoyuan
  • Cai, Min

Abstract

This paper considers an efficient and accurate spectral deferred correction (SDC) method for the initial value problem (IVP) with Caputo–Hadamard derivative. We first apply the basic idea of the SDC method to derive the numerical scheme. Then the iteration matrix which is the key to convergence of the proposed scheme can be obtained for the linear problem. Detailed computation of history term is presented using the spectral collocation method based on mapped Jacobi log orthogonal functions (MJLOFs). Finally, numerical simulations for both linear and nonlinear cases are shown to verify the feasibility and efficiency of the proposed method.

Suggested Citation

  • Liu, Xiaoyuan & Cai, Min, 2024. "Spectral deferred correction method for fractional initial value problem with Caputo–Hadamard derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 323-337.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:323-337
    DOI: 10.1016/j.matcom.2024.07.007
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    1. Liu, Yang & Ran, Maohua, 2024. "Arbitrarily high-order explicit energy-conserving methods for the generalized nonlinear fractional Schrödinger wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 126-144.
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