Implicit Runge-Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian
DOI10.1002/num.23074MaRDI QIDQ6556882
Yanming Zhang, Yuexin Yu, Wansheng Wang, Yu Li
Publication date: 17 June 2024
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
stabilityconvergenceimplicit Runge-Kutta methodspectral Galerkin methodfractional diffusion equationspectral fractional Laplacian
Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
- Unnamed Item
- A PDE approach to fractional diffusion: a posteriori error analysis
- Fourier spectral methods for fractional-in-space reaction-diffusion equations
- Nonhomogeneous boundary conditions for the spectral fractional Laplacian
- Fourierization of the Legendre-Galerkin method and a new space-time spectral method
- Nonlinear stability of explicit and diagonally implicit Runge-Kutta methods for neutral delay differential equations in Banach space
- Unconditional convergence of DIRK schemes applied to dissipative evolution equations
- Fractional powers of dissipative operators
- Potential theory of subordinate killed Brownian motion in a domain
- The finite difference method for Caputo-type parabolic equation with fractional Laplacian: one-dimension case
- A fast algorithm for solving the space-time fractional diffusion equation
- Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation
- Efficient spectral methods for PDEs with spectral fractional Laplacian
- General linear and spectral Galerkin methods for the nonlinear two-sided space distributed-order diffusion equation
- Lie-Trotter operator splitting spectral method for linear semiclassical fractional Schrödinger equation
- Fractional centered difference scheme for high-dimensional integral fractional Laplacian
- Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation
- What is the fractional Laplacian? A comparative review with new results
- A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations
- Diagonally implicit Runge-Kutta methods for stiff ODEs
- A Fourier spectral method for fractional-in-space Cahn-Hilliard equation
- An efficient and accurate numerical method for the spectral fractional Laplacian equation
- On sinc quadrature approximations of fractional powers of regularly accretive operators
- A PDE approach to fractional diffusion in general domains: a priori error analysis
- A PDE approach to space-time fractional parabolic problems
- Rational Approximation to the Fractional Laplacian Operator in Reaction-Diffusion Problems
- An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
- Variational solution of fractional advection dispersion equations on bounded domains in ℝd
- Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
- Highest possible order of algebraically stable diagonally implicit runge-kutta methods
- Analysis of Spectral Projectors in One-Dimensional Domains
- Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
- Analysis and Approximation of a Fractional Cahn--Hilliard Equation
- A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$
- Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations
- An Extension Problem Related to the Fractional Laplacian
- Multilevel methods for nonuniformly elliptic operators and fractional diffusion
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