A high-order difference scheme for the space and time fractional Bloch-Torrey equation

DOI10.1515/CMAM-2017-0034zbMath1382.65262OpenAlexW2751117820MaRDI QIDQ1697115

Yun Zhu, Zhi-zhong Sun

Publication date: 15 February 2018

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/cmam-2017-0034

zbMATH Keywords

stabilityconvergencenumerical examplefinite difference schemefractional derivativeBloch-Torrey equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Fractional partial differential equations (35R11)

Related Items (3)

A bilateral preconditioning for an L2-type all-at-once system from time-space non-local evolution equations with a weakly singular kernel ⋮ Numerical algorithms for the time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations ⋮ Fast and efficient finite difference/finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equation

Cites Work

• Unnamed Item
• Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations
• A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• Too much regularity may force too much uniqueness
• Fractional Bloch equation with delay
• Some high order difference schemes for the space and time fractional Bloch-Torrey equations
• A high-order compact finite difference scheme for the fractional sub-diffusion equation
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Time fractional diffusion: A discrete random walk approach
• A computationally effective alternating direction method for the space and time fractional Bloch-Torrey equation in 3-D
• Stability and convergence of an implicit numerical method for the space and time fractional Bloch–Torrey equation
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• A class of second order difference approximations for solving space fractional diffusion equations
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

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