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Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation

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  • Alikhanov, Anatoly A.

Abstract

Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using the method of the energy inequalities. The stability and convergence of the difference schemes follow from a priory estimates. The credibility of the obtained results is verified by performing numerical calculations for test problems.

Suggested Citation

  • Alikhanov, Anatoly A., 2015. "Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 12-22.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:12-22
    DOI: 10.1016/j.amc.2015.06.045
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    Cited by:

    1. Wang, Yuan-Ming & Wen, Xin, 2020. "A compact exponential difference method for multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    2. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Alikhanov, Anatoly A. & Huang, Chengming, 2021. "A high-order L2 type difference scheme for the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    5. Zheng, Xiangcheng & Jia, Jinhong & Guo, Xu, 2023. "Eliminating solution singularity of variably distributed-order time-fractional diffusion equation via strongly singular initial distribution," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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