On \(\tau\)-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations
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Publication:6176692
DOI10.1016/j.camwa.2023.06.015OpenAlexW4382047254MaRDI QIDQ6176692
Wei Qu, Siu-Long Lei, Yuan-Yuan Huang
Publication date: 23 August 2023
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2023.06.015
spectral analysispreconditioned conjugate gradient methodstability and convergenceRiesz space-fractional diffusion equations\(\tau\)-preconditioner
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) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11)
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Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation, Two fast and unconditionally stable finite difference methods for Riesz fractional diffusion equations with variable coefficients
Cites Work
- Unnamed Item
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- High-order algorithms for Riesz derivative and their applications. III
- Low-rank solvers for fractional differential equations
- Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
- High-order algorithms for Riesz derivative and their applications. II
- A fast method for a generalized nonlocal elastic model
- A circulant preconditioner for fractional diffusion equations
- Multigrid method for fractional diffusion equations
- Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
- A fourth-order approximation of fractional derivatives with its applications
- Spectral analysis and structure preserving preconditioners for fractional diffusion equations
- Spectral and computational properties of band symmetric Toeplitz matrices
- Riesz potential operators and inverses via fractional centred derivatives
- High-order compact ADI methods for parabolic equations
- Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
- High-order numerical algorithms for Riesz derivatives via constructing new generating functions
- Waiting-times and returns in high-frequency financial data: An empirical study
- Finite difference approximations for fractional advection-dispersion flow equations
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- Numerical analysis and fast implementation of a fourth-order difference scheme for two-dimensional space-fractional diffusion equations
- Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients
- Efficient second-order ADI difference schemes for three-dimensional Riesz space-fractional diffusion equations
- Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations
- On \(\tau\) matrix-based approximate inverse preconditioning technique for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations
- A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations
- A preconditioner based on sine transform for space fractional diffusion equations
- A class of unconditioned stable 4-point WSGD schemes and fast iteration methods for space fractional diffusion equations
- An explicit structure-preserving algorithm for the nonlinear fractional Hamiltonian wave equation
- A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations
- A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation
- All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations
- Fast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equations
- Symplectic scheme for the Schrödinger equation with fractional Laplacian
- A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
- Finite difference approximations for two-sided space-fractional partial differential equations
- A fast gradient projection method for a constrained fractional optimal control
- Developing and analyzing fourth-order difference methods for the metamaterial Maxwell's equations
- Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner
- Superlinear PCG methods for symmetric Toeplitz systems
- Conjugate Gradient Methods for Toeplitz Systems
- Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations
- Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations
- Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations
- 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
- Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
- High‐order algorithms for Riesz derivative and their applications (V)
- Multilevel Circulant Preconditioner for High-Dimensional Fractional Diffusion Equations
- Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators
- Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations
- An Introduction to Iterative Toeplitz Solvers
- Preconditioners for fractional diffusion equations based on the spectral symbol
