A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains
From MaRDI portal
Publication:2047609
DOI10.1016/j.camwa.2021.06.013zbMath1504.65188OpenAlexW3185048041MaRDI QIDQ2047609
Mengchen Zhang, Fawang Liu, Ian W. Turner, V. V. Anh, L. B. Feng
Publication date: 20 August 2021
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2021.06.013
finite volume methodnon-smooth solutionsvariable coefficientsBloch-Torrey equationvariable-order fractional derivative
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)
Related Items
A vertex-centred finite volume method for the 3D multi-term time and space fractional Bloch-Torrey equation with fractional Laplacian, Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators, Galerkin finite element method for a two-dimensional tempered time-space fractional diffusion equation with application to a Bloch-Torrey equation retaining Larmor precession, The non-uniform L1-type scheme coupling the finite volume method for the time-space fractional diffusion equation with variable coefficients, An energy-preserving computational approach for the semilinear space fractional damped Klein-Gordon equation with a generalized scalar potential
Cites Work
- Unnamed Item
- An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations
- A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging
- Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
- Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations
- Mittag-Leffler functions and their applications
- On the selection and meaning of variable order operators for dynamic modeling
- Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
- Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
- An efficient technique based on finite difference/finite element method for solution of two-dimensional space/multi-time fractional Bloch-Torrey equations
- Reprint of: boundary conditions for fractional diffusion
- The role of fractional calculus in modeling biological phenomena: a review
- Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging
- Can fractional calculus help improve tumor growth models?
- Unstructured-mesh Galerkin finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equations on irregular convex domains
- A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements
- An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media
- An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains
- A tunable finite difference method for fractional differential equations with non-smooth solutions
- Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
- Boundary conditions for two-sided fractional diffusion
- Modelling anomalous diffusion using fractional Bloch-Torrey equations on approximate irregular domains
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- Discretized Fractional Calculus
- Modeling the Cardiac Tissue Electrode Interface Using Fractional Calculus
- Integration and differentiation to a variable fractional order
- Applications of variable-order fractional operators: a review
