An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation

DOI10.1007/s11425-022-2094-xMaRDI QIDQ6616475

Wei Zeng, Chuanju Xu

Publication date: 9 October 2024

Published in: Science China. Mathematics (Search for Journal in Brave)

zbMATH Keywords

variable transformationwell-posednesserror estimatefast algorithmsubdiffusion equations\(\psi\)-Sobolev spacesspace-time Galerkin spectral method

Mathematics Subject Classification ID

Numerical analysis (65-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• A new difference scheme for the time fractional diffusion equation
• A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions
• Fourierization of the Legendre-Galerkin method and a new space-time spectral method
• Generalized Jacobi polynomials/functions and their applications
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A stable fast time-stepping method for fractional integral and derivative operators
• A unified Petrov-Galerkin spectral method for fractional PDEs
• An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
• A fractional spectral method with applications to some singular problems
• Müntz spectral methods for the time-fractional diffusion equation
• A Caputo fractional derivative of a function with respect to another function
• A posteriori error estimates of spectral method for the fractional optimal control problems with non-homogeneous initial conditions
• Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
• An efficient space-time method for time fractional diffusion equation
• Finite difference/spectral approximations for the time-fractional diffusion equation
• High-order accurate adaptive kernel compression time-stepping schemes for fractional differential equations
• A fully discrete difference scheme for a diffusion-wave system
• Generalized Jacobi functions and their applications to fractional differential equations
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• A Kernel Compression Scheme for Fractional Differential Equations
• Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
• Convolution quadrature time discretization of fractional diffusion-wave equations
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
• Numerical solution to a linearized time fractional KdV equation on unbounded domains
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions
• Log orthogonal functions: approximation properties and applications
• A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
• Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

This page was built for publication: An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation