Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation
From MaRDI portal
Publication:970584
DOI10.1007/s11075-009-9320-1zbMath1191.65116OpenAlexW2033471049MaRDI QIDQ970584
Ian W. Turner, Chang-Ming Chen, V. V. Anh, Fawang Liu
Publication date: 19 May 2010
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://eprints.qut.edu.au/29756/1/c29756.pdf
stabilityconvergencefinite difference methodnumerical examplesanomalous sub-diffusion equationmultivariate extrapolation
Heat equation (35K05) 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)
Related Items
A novel ADI Galerkin spectral element method for the solution of two-dimensional time fractional subdiffusion equation ⋮ Wavelet based algorithm for numerical study of \((1+2)\)-dimensional time fractional diffusion problems ⋮ Numerical simulation for the three-dimension fractional sub-diffusion equation ⋮ Crank-Nicolson ADI Galerkin finite element method for two-dimensional fractional Fitzhugh-Nagumo monodomain model ⋮ Three-point combined compact difference schemes for time-fractional advection-diffusion equations with smooth solutions ⋮ Numerical method with high order accuracy for solving a anomalous subdiffusion equation ⋮ A modified compact ADI method and its extrapolation for two-dimensional fractional subdiffusion equations ⋮ Error analysis of a high-order compact ADI method for two-dimensional fractional convection-subdiffusion equations ⋮ A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation ⋮ Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation ⋮ An unconditionally stable compact ADI method for three-dimensional time-fractional convection-diffusion equation ⋮ Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations ⋮ Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain ⋮ Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory ⋮ Two alternating direction implicit difference schemes for two-dimensional distributed-order fractional diffusion equations ⋮ A weighted ADI scheme for subdiffusion equations ⋮ A new implicit compact difference scheme for the fourth-order fractional diffusion-wave system ⋮ Numerical algorithm with high spatial accuracy for the fractional diffusion-wave equation with von Neumann boundary conditions ⋮ High-order compact difference methods for Caputo-type variable coefficient fractional sub-diffusion equations in conservative form ⋮ High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation ⋮ Numerical methods for time-fractional convection-diffusion problems with high-order accuracy ⋮ A hybridizable discontinuous Galerkin method for fractional diffusion problems ⋮ A compact finite difference scheme for the fractional sub-diffusion equations ⋮ The long time error analysis in the second order difference type method of an evolutionary integral equation with completely monotonic kernel ⋮ Numerical methods for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion ⋮ Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation ⋮ Two-dimensional nonlinear time fractional reaction-diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media ⋮ Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation ⋮ Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation ⋮ Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation ⋮ An efficient iterative approach for three-dimensional modified anomalous fractional sub-diffusion equations on a large domain ⋮ An alternating segment Crank-Nicolson parallel difference scheme for the time fractional sub-diffusion equation ⋮ A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term ⋮ Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation ⋮ A compact ADI method and its extrapolation for time fractional sub-diffusion equations with nonhomogeneous Neumann boundary conditions ⋮ The high-order compact numerical algorithms for the two-dimensional fractional sub-diffusion equation ⋮ Numerical asymptotic stability for the integro-differential equations with the multi-term kernels ⋮ Efficient and stable numerical methods for the two-dimensional fractional Cattaneo equation ⋮ A compact locally one-dimensional method for fractional diffusion-wave equations ⋮ The implicit midpoint method for the modified anomalous sub-diffusion equation with a nonlinear source term ⋮ FINITE DIFFERENCE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS ⋮ Maximum norm error estimates of ADI methods for a two-dimensional fractional subdiffusion equation ⋮ Implicit compact difference schemes for the fractional cable equation ⋮ A finite difference method for an anomalous sub-diffusion equation, theory and applications ⋮ Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations ⋮ A compact LOD method and its extrapolation for two-dimensional modified anomalous fractional sub-diffusion equations ⋮ A novel compact ADI scheme for the time-fractional subdiffusion equation in two space dimensions ⋮ Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems ⋮ Obtaining artificial boundary conditions for fractional sub-diffusion equation on space two-dimensional unbounded domains ⋮ Uniform \(l^1\) behavior in the Crank-Nicolson methods for a linear Volterra equation with convex kernel ⋮ Lattice Boltzmann model for time sub-diffusion equation in Caputo sense ⋮ Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations ⋮ Numerical Solution of Fractional Diffusion-Wave Equation ⋮ The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence ⋮ Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation ⋮ Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation ⋮ A high-order numerical scheme based on graded mesh and its analysis for the two-dimensional time-fractional convection-diffusion equation ⋮ A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation ⋮ Time-stepping discontinuous Galerkin methods for fractional diffusion problems ⋮ Numerical methods for fractional partial differential equations
Cites Work
- Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation
- Implicit difference approximation for the time fractional diffusion equation
- Large deviations for local time fractional Brownian motion and applications
- Particle tracking for fractional diffusion with two time scales
- Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
- Anomalous diffusion in one dimension
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- Finite difference approximations for fractional advection-dispersion flow equations
- A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second-grade fluid with fractional derivative
- Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second-grade fluid with fractional derivatives
- A Fourier method for the fractional diffusion equation describing sub-diffusion
- Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation
- Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\)
- Fractional diffusion and wave equations
- Convolution quadrature time discretization of fractional diffusion-wave equations
- Variational solution of fractional advection dispersion equations on bounded domains in ℝd
- New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
- The fractional diffusion equation
- An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
- Fractional diffusion: probability distributions and random walk models
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
- Unnamed Item