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A Lagrange-quadratic spline optimal collocation method for the time tempered fractional diffusion equation

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  • Luo, Wei-Hua
  • Gu, Xian-Ming
  • Yang, Liu
  • Meng, Jing

Abstract

In the current paper, for the time fractional diffusion equation with an exponential tempering, we propose a numerical algorithm based on the Lagrange-quadratic spline interpolations and the optimal technique. The discretized linear systems and some properties are investigated in detail. By using these properties, the coefficient matrix and the right-hand term at each time step are given to analyze the computational cost. Theoretical analyses show that this proposed method enjoys both stability and convergence order of O(τ2+h4). Some numerical examples are provided to verify the practical feasibility and efficiency of the proposed scheme.

Suggested Citation

  • Luo, Wei-Hua & Gu, Xian-Ming & Yang, Liu & Meng, Jing, 2021. "A Lagrange-quadratic spline optimal collocation method for the time tempered fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 1-24.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:1-24
    DOI: 10.1016/j.matcom.2020.10.016
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    References listed on IDEAS

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    1. Sun, Xiaorui & Li, Can & Zhao, Fengqun, 2020. "Local discontinuous Galerkin methods for the time tempered fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    2. Meilan Qiu & Dewang Li & Yanyun Wu, 2020. "Local Discontinuous Galerkin Method for Nonlinear Time-Space Fractional Subdiffusion/Superdiffusion Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-21, June.
    3. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
    4. Alvaro Cartea & Diego del-Castillo-Negrete, 2007. "On the Fluid Limit of the Continuous-Time Random Walk with General Lévy Jump Distribution Functions," Birkbeck Working Papers in Economics and Finance 0708, Birkbeck, Department of Economics, Mathematics & Statistics.
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    Cited by:

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    2. Samad Noeiaghdam & Sanda Micula, 2021. "A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel," Mathematics, MDPI, vol. 9(17), pages 1-12, September.

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