A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation
From MaRDI portal
Publication:316084
DOI10.1016/j.camwa.2013.01.048zbMath1346.35219OpenAlexW2142031974MaRDI QIDQ316084
Qianqian Yang, Timothy J. Moroney
Publication date: 26 September 2016
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2013.01.048
finite differencesmethod of linesnonlinearbanded preconditionerJacobian-free Newton-Krylovtwo-sided fractional diffusion
Related Items
A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations ⋮ Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners ⋮ Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns ⋮ On CSCS-based iteration method for tempered fractional diffusion equations ⋮ Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy ⋮ Computational challenge of fractional differential equations and the potential solutions: a survey ⋮ A matrix splitting preconditioning method for solving the discretized tempered fractional diffusion equations ⋮ Efficient Preconditioner Updates for Semilinear Space–Time Fractional Reaction–Diffusion Equations ⋮ Fully Finite Element Adaptive AMG Method for Time-Space Caputo-Riesz Fractional Diffusion Equations ⋮ Fast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equations ⋮ Stability and convergence of a finite volume method for the space fractional advection-dispersion equation ⋮ An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains ⋮ A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices ⋮ Adaptive finite element method for fractional differential equations using hierarchical matrices ⋮ Tensor-train format solution with preconditioned iterative method for high dimensional time-dependent space-fractional diffusion equations with error analysis
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- SUNDIALS
- An implicit RBF meshless approach for time fractional diffusion equations
- Multigrid method for fractional diffusion equations
- Fourier spectral methods for fractional-in-space reaction-diffusion equations
- Fractional calculus for scientists and engineers.
- A second-order accurate numerical method for the two-dimensional fractional diffusion equation
- Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
- Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
- Numerical solution of the space fractional Fokker-Planck equation.
- Finite difference approximations for fractional advection-dispersion flow equations
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- Stability and convergence of a finite volume method for the space fractional advection-dispersion equation
- Finite difference methods for two-dimensional fractional dispersion equation
- Finite difference approximations for two-sided space-fractional partial differential equations
- AN ADVANCED MESHLESS METHOD FOR TIME FRACTIONAL DIFFUSION EQUATION
- Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
- An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- New Trends in Nanotechnology and Fractional Calculus Applications
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Sparse Matrices in MATLAB: Design and Implementation
- Solving Nonlinear Equations with Newton's Method
- Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions
- Variational formulation for the stationary fractional advection dispersion equation
- Stochastic models for fractional calculus
