Spectral method for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain

DOI10.1016/j.cam.2021.113712zbMath1500.65087OpenAlexW3179760003MaRDI QIDQ2050928

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

Publication date: 1 September 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113712

zbMATH Keywords

Gauss quadrature formulastability and convergence analysisa semi-infinite domainADI Legendre-Laguerre spectral methodtwo-dimensional time distributed-order diffusion-wave equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Hydrology, hydrography, oceanography (86A05) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Wave equation (35L05) 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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical quadrature and cubature formulas (65D32) Fractional partial differential equations (35R11)

Related Items (11)

Fast method and convergence analysis for the magnetohydrodynamic flow and heat transfer of fractional Maxwell fluid ⋮ L1 method on nonuniform meshes for linear time-fractional diffusion equations with constant time delay ⋮ Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems ⋮ An easy to implement linearized numerical scheme for fractional reaction-diffusion equations with a prehistorical nonlinear source function ⋮ Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation ⋮ Novel and accurate Gegenbauer spectral tau algorithms for distributed order nonlinear time-fractional telegraph models in multi-dimensions ⋮ Discrete Chebyshev polynomials for the numerical solution of stochastic fractional two-dimensional Sobolev equation ⋮ Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions ⋮ Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain ⋮ Numerical solving of nonlinear differential equations using a hybrid method on a semi-infinite interval ⋮ Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation
• Space-fractional advection-dispersion equations by the Kansa method
• Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem
• Spectral direction splitting methods for two-dimensional space fractional diffusion equations
• Harmonic analysis of random fractional diffusion-wave equations.
• A new fractional finite volume method for solving the fractional diffusion equation
• Finite difference/spectral approximations to a water wave model with a nonlocal viscous term
• New compact difference scheme for solving the fourth-order time fractional sub-diffusion equation of the distributed order
• Local discontinuous Galerkin method for distributed-order time and space-fractional convection-diffusion and Schrödinger-type equations
• Chaos, fractional kinetics, and anomalous transport
• Waiting-times and returns in high-frequency financial data: An empirical study
• Spectral methods for the time fractional diffusion-wave equation in a semi-infinite channel
• Fast numerical simulation of a new time-space fractional option pricing model governing European call option
• Two alternating direction implicit difference schemes for solving the two-dimensional time distributed-order wave equations
• Error analysis of a finite difference method on graded meshes for a multiterm time-fractional initial-boundary value problem
• Legendre spectral element method for solving time fractional modified anomalous sub-diffusion equation
• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
• Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains
• Finite difference/finite element methods for distributed-order time fractional diffusion equations
• New study of weakly singular kernel fractional fourth-order partial integro-differential equations based on the optimum \(q\)-homotopic analysis method
• A semi-linear delayed diffusion-wave system with distributed order in time
• Distributed order calculus and equations of ultraslow diffusion
• Stochastic model for ultraslow diffusion
• Existence of Turing Instabilities in a Two-Species Fractional Reaction-Diffusion System
• Fast Finite Difference Approximation for Identifying Parameters in a Two-dimensional Space-fractional Nonlocal Model with Variable Diffusivity Coefficients
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• Spectral Methods
• Distributed-Order Dynamic Systems
• Applications of Fractional Calculus to the Theory of Viscoelasticity
• Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• 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
• A Laguerre–Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Stochastic models for fractional calculus
• Analysis of fractional differential equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Spectral method for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain