Finite difference/generalized Hermite spectral method for the distributed-order time-fractional reaction-diffusion equation on multi-dimensional unbounded domains

DOI10.1016/j.camwa.2021.04.002OpenAlexW3156831858MaRDI QIDQ2027566

Shimin Guo, Yaping Chen, Yining Song, Liquan Mei

Publication date: 27 May 2021

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.04.002

zbMATH Keywords

unbounded domainfinite differencestability and convergencedistributed-order fractional derivativegeneralized Hermite functions

Mathematics Subject Classification ID

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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Related Items (1)

A suitable hybrid meshless method for the numerical solution of time-fractional fourth-order reaction-diffusion model in the multi-dimensional case

Cites Work

• Unnamed Item
• A new difference scheme for the time fractional diffusion equation
• Generalized Hermite approximations and spectral method for partial differential equations in multiple dimensions
• Some results on determinants and inverses of nonsingular pentadiagonal matrices
• A difference method for solving the Steklov nonlocal boundary value problem of second kind for the time-fractional diffusion equation
• Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method
• Fractional calculus in viscoelasticity: an experimental study
• Fractional Sturm-Liouville boundary value problems in unbounded domains: theory and applications
• Numerical analysis for distributed-order differential equations
• The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations
• A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
• Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation
• A finite difference/finite element technique with error estimate for space fractional tempered diffusion-wave equation
• Existence and uniqueness of a weak solution to a non-autonomous time-fractional diffusion equation (of distributed order)
• Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations
• A variably distributed-order time-fractional diffusion equation: analysis and approximation
• Application of spectral element method for solving Sobolev equations with error estimation
• Alternating direction implicit-spectral element method (ADI-SEM) for solving multi-dimensional generalized modified anomalous sub-diffusion equation
• Rational pseudospectral approximation to the solution of a nonlinear integro-differential equation arising in modeling of the population growth
• Deterministic analysis of distributed order systems using operational matrix
• Legendre spectral element method for solving time fractional modified anomalous sub-diffusion equation
• Finite difference/Hermite-Galerkin spectral method for multi-dimensional time-fractional nonlinear reaction-diffusion equation in unbounded domains
• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
• Some high-order difference schemes for the distributed-order differential equations
• Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain
• Numerical solution of distributed order fractional differential equations by hybrid functions
• Fractional spectral and pseudo-spectral methods in unbounded domains: theory and applications
• Generalized Hermite Spectral Method and its Applications to Problems in Unbounded Domains
• Spectral Methods
• Distributed-Order Dynamic Systems
• The Hermite Spectral Method for Gaussian-Type Functions
• 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
• Petrov--Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations
• Hermite Spectral Methods for Fractional PDEs in Unbounded Domains
• Generalized Laguerre Interpolation and Pseudospectral Method for Unbounded Domains
• On Direct Methods for Solving Poisson’s Equations
• Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains
• An efficient finite difference/Hermite-Galerkin spectral method for time-fractional coupled sine-Gordon equations on multidimensional unbounded domains and its application in numerical simulations of vector solitons

This page was built for publication: Finite difference/generalized Hermite spectral method for the distributed-order time-fractional reaction-diffusion equation on multi-dimensional unbounded domains