A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation

DOI10.1016/j.camwa.2018.08.042zbMath1442.65301OpenAlexW2891419498WikidataQ129234661 ScholiaQ129234661MaRDI QIDQ2203014

Hui Zhang, Fanhai Zeng, Fawang Liu, Ian W. Turner, Xiao-yun Jiang

Publication date: 1 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.08.042

zbMATH Keywords

Gauss quadraturestability and convergence analysisADI Galerkin-Legendre spectral methodtwo-dimensional Riesz space distributed-order advection-diffusion equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items

Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations, Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equation, Fast second-order time two-mesh mixed finite element method for a nonlinear distributed-order sub-diffusion model, General linear and spectral Galerkin methods for the nonlinear two-sided space distributed-order diffusion equation, A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives, The application of the distributed-order time fractional Bloch model to magnetic resonance imaging, High-order numerical method for solving a space distributed-order time-fractional diffusion equation, Numerical investigation of reproducing kernel particle Galerkin method for solving fractional modified distributed-order anomalous sub-diffusion equation with error estimation, Implicit Runge-Kutta and spectral Galerkin methods for Riesz space fractional/distributed-order diffusion equation, An investigation of radial basis functions for fractional derivatives and their applications, The direct meshless local Petrov-Galerkin technique with its error estimate for distributed-order time fractional cable equation, The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: numerical analysis, A fourth‐order accurate numerical method for the distributed‐order Riesz space fractional diffusion equation, A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation, A study of distributed‐order time fractional diffusion models with continuous distribution weight functions, A novel distributed order time fractional model for heat conduction, anomalous diffusion, and viscoelastic flow problems, High-order orthogonal spline collocation ADI scheme for a new complex two-dimensional distributed-order fractional integro-differential equation with two weakly singular kernels, Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation, Numerical study of distributed-order Bessel fractional derivative with application to Euler-Poisson-Darboux equation, A novel finite element method for the distributed-order time fractional Cable equation in two dimensions, Local discontinuous Galerkin method for a hidden-memory variable order reaction-diffusion equation, A distributed‐order fractional diffusion equation with a singular density function: Analysis and approximation, A hybrid fourth order time stepping method for space distributed order nonlinear reaction-diffusion equations, Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions, Numerical solution of distributed-order fractional 2D optimal control problems using the Bernstein polynomials, Stability analysis of difference-Legendre spectral method for two-dimensional Riesz space distributed-order diffusion-wave model, Multi-output physics-informed neural network for one- and two-dimensional nonlinear time distributed-order models, BDF2 ADI orthogonal spline collocation method for the fractional integro-differential equations of parabolic type in three dimensions, Optimal order finite difference/local discontinuous Galerkin method for variable-order time-fractional diffusion equation, Utilizing differential quadrature-based RBF partition of unity collocation method to simulate distributed-order time fractional cable equation, A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation, A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equation, A novel finite volume method for the nonlinear two-sided space distributed-order diffusion equation with variable coefficients, A Crank-Nicolson ADI quadratic spline collocation method for two-dimensional Riemann-Liouville space-fractional diffusion equations, An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain, Necessity of introducing non-integer shifted parameters by constructing high accuracy finite difference algorithms for a two-sided space-fractional advection-diffusion model, TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation, Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations, An efficient split-step method for distributed-order space-fractional reaction-diffusion equations with time-dependent boundary conditions, Finite volume approximation with ADI scheme and low-rank solver for high dimensional spatial distributed-order fractional diffusion equations, Flow and heat transfer of viscoelastic fluid with a novel space distributed-order constitution relationship, Approximation methods for the distributed order calculus using the convolution quadrature, Modeling and computing of fractional convection equation, A Galerkin finite element method for the modified distributed-order anomalous sub-diffusion equation, Temporal second-order difference methods for solving multi-term time fractional mixed diffusion and wave equations, Space-time finite element method for the distributed-order time fractional reaction diffusion equations, Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation, Error estimate of a fully discrete local discontinuous Galerkin method for variable-order time-fractional diffusion equations, Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media, Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation, Memory dependent anomalous diffusion in comb structure under distributed order time fractional dual-phase-lag model, An Efficient Second-Order Finite Volume ADI Method for Nonlinear Three-Dimensional Space-Fractional Reaction-Diffusion Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations
• An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation
• An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate
• Two-dimensional Legendre wavelet method for travelling wave solutions of time-fractional generalized seventh order KdV equation
• Anomalous diffusion modeling by fractal and fractional derivatives
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Numerical solution of the three-dimensional advection--diffusion equation.
• Numerical solution of the space fractional Fokker-Planck equation.
• A new ADI technique for two-dimensional parabolic equation with an integral condition
• Finite difference/spectral approximations to a water wave model with a nonlocal viscous term
• A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
• A novel finite volume method for the Riesz space distributed-order diffusion equation
• Variable order and distributed order fractional operators
• Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
• A novel finite volume method for the Riesz space distributed-order advection-diffusion equation
• A Fourier spectral method for fractional-in-space Cahn-Hilliard equation
• A high-order spectral method for the multi-term time-fractional diffusion equations
• Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains
• Fourth-order numerical method for the space-time tempered fractional diffusion-wave equation
• A time-space spectral method for the time-space fractional Fokker-Planck equation and its inverse problem
• A fictitious domain approach to the numerical solution of PDEs in stochastic domains
• Numerical identification of the fractional derivatives in the two-dimensional fractional cable equation
• Fast Finite Difference Approximation for Identifying Parameters in a Two-dimensional Space-fractional Nonlocal Model with Variable Diffusivity Coefficients
• Spectral Methods
• Distributed-Order Dynamic Systems
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• 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 Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• UNIFORM INF–SUP CONDITIONS FOR THE SPECTRAL DISCRETIZATION OF THE STOKES PROBLEM
• A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed‐order fractional damped diffusion‐wave equation
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• Solving nonlinear fractional partial differential equations using the homotopy analysis method
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation
• Petrov--Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations
• DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION