Anatoly A. Alikhanov

Publication Activity (10 Years)

Years Active: 2012-2024
Publications (10 Years): 23

Top Topics

Diffusion Equation

Boundary Value Problem

Numerical Analysis

Top Venues

J. Comput. Appl. Math.

Comput. Methods Appl. Math.

J. Sci. Comput.

Publications

Nikki Kedia, Anatoly A. Alikhanov, Vineet Kumar Singh
Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution. Math. Comput. Simul. 219 (2024)
Abhishek Kumar Singh, Mani Mehra, Anatoly A. Alikhanov
Modified least squares method and a review of its applications in machine learning and fractional differential/integral equations. CoRR (2024)
Anatoly A. Alikhanov, Mohammad Shahbazi Asl, Chengming Huang, Aslanbek Khibiev
A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay. J. Comput. Appl. Math. 438 (2024)
Aslanbek Khibiev, Anatoly A. Alikhanov, Chengming Huang
A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions. Comput. Methods Appl. Math. 24 (1) (2024)
Guoyu Zhang, Chengming Huang, Anatoly A. Alikhanov, Baoli Yin
A High-Order Discrete Energy Decay and Maximum-Principle Preserving Scheme for Time Fractional Allen-Cahn Equation. J. Sci. Comput. 96 (2) (2023)
Aleksei Tyrylgin, Maria V. Vasilyeva, Anatoly A. Alikhanov, Dongwoo Sheen
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media. J. Comput. Appl. Math. 418 (2023)
Guoyu Zhang, Chengming Huang, Anatoly A. Alikhanov, Baoli Yin
A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation. CoRR (2023)
Anatoly A. Alikhanov, Mohammad Shahbazi Asl, Chengming Huang
Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation. CoRR (2023)
Anatoly A. Alikhanov, Chengming Huang
A class of time-fractional diffusion equations with generalized fractional derivatives. J. Comput. Appl. Math. 414 (2022)
Wenyuan Li, Anatoly A. Alikhanov, Yalchin Efendiev, Wing Tat Leung
Partially explicit time discretization for nonlinear time fractional diffusion equations. Commun. Nonlinear Sci. Numer. Simul. 113 (2022)
Abhishek Kumar Singh, Mani Mehra, Anatoly A. Alikhanov
Data-Driven Discovery of Time Fractional Differential Equations. ICCS (1) (2022)
Anatoly A. Alikhanov, Chengming Huang
A high-order L2 type difference scheme for the time-fractional diffusion equation. Appl. Math. Comput. 411 (2021)
Aslanbek Khibiev, Anatoly A. Alikhanov, Chengming Huang
A second order difference scheme for time fractional diffusion equation with generalized memory kernel. CoRR (2021)
Mahmoud A. Zaky, Ahmed S. Hendy, Anatoly A. Alikhanov, Vladimir G. Pimenov
Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: What could possibly go wrong? Commun. Nonlinear Sci. Numer. Simul. 96 (2021)
Anatoly A. Alikhanov, Chengming Huang
A high-order L2 type difference scheme for the time-fractional diffusion equation. CoRR (2021)
Ruilian Du, Anatoly A. Alikhanov, Zhi-Zhong Sun
Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations. Comput. Math. Appl. 79 (10) (2020)
Guang-hua Gao, Anatoly A. Alikhanov, Zhi-Zhong Sun
The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for Solving the Time Multi-term and Distributed-Order Fractional Sub-diffusion Equations. J. Sci. Comput. 73 (1) (2017)
Xian-Ming Gu, Ting-Zhu Huang, Cui-Cui Ji, Bruno Carpentieri, Anatoly A. Alikhanov
Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection-Diffusion Equation. J. Sci. Comput. 72 (3) (2017)
Anatoly A. Alikhanov
A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions. Comput. Methods Appl. Math. 17 (4) (2017)
Anatoly A. Alikhanov
A Difference Method for Solving the Steklov Nonlocal Boundary Value Problem of Second Kind for the Time-Fractional Diffusion Equation. Comput. Methods Appl. Math. 17 (1) (2017)
Anatoly A. Alikhanov, Inna Z. Kodzokova
A Higher Order Difference Scheme for the Time Fractional Diffusion Equation with the Steklov Nonlocal Boundary Value Problem of the Second Kind. NAA (2016)
Anatoly A. Alikhanov
A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280 (2015)
Anatoly A. Alikhanov
Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation. Appl. Math. Comput. 268 (2015)
Anatoly A. Alikhanov
Boundary value problems for the diffusion equation of the variable order in differential and difference settings. Appl. Math. Comput. 219 (8) (2012)