Finite difference method on non-uniform meshes for time fractional diffusion problem

DOI10.1515/CMAM-2020-0077zbMath1476.65187OpenAlexW3117101818MaRDI QIDQ823681

Aijie Cheng, Haili Qiao

Publication date: 16 December 2021

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

Full work available at URL: https://doi.org/10.1515/cmam-2020-0077

zbMATH Keywords

finite differencenon-uniform meshesfractional differential equationweak singularityAlikhanov scheme

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) Fractional partial differential equations (35R11)

Related Items (1)

A novel high-order finite-difference method for the time-fractional diffusion equation with smooth/nonsmooth solutions

Cites Work

• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• Finite difference methods for the time fractional diffusion equation on non-uniform meshes
• A new difference scheme for the time fractional diffusion equation
• Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
• Too much regularity may force too much uniqueness
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• A compact finite difference scheme for the fractional sub-diffusion equations
• Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
• Implicit difference approximation for the time fractional diffusion equation
• Numerical simulations of 2D fractional subdiffusion problems
• An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
• Some time stepping methods for fractional diffusion problems with nonsmooth data
• A higher order numerical method for time fractional partial differential equations with nonsmooth data
• Time fractional diffusion: A discrete random walk approach
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• Nonpolynomial collocation approximation of solutions to fractional differential equations
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• Optimal Error Estimates of Spectral Petrov--Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations
• Random Walks on Lattices. II
• A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
• A High Order Method on Graded Meshes for a Time-Fractional Diffusion Problem
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

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