A second-order energy stable and nonuniform time-stepping scheme for time fractional Burgers' equation
DOI10.1016/j.camwa.2022.08.007OpenAlexW4293156003WikidataQ113878656 ScholiaQ113878656MaRDI QIDQ2079741
Jincheng Ren, Shanzhen Chen, Jin-ye Shen
Publication date: 30 September 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2022.08.007
graded meshweak singularityfast convolution algorithmfractional Burgers' equationa second-order scheme
KdV equations (Korteweg-de Vries equations) (35Q53) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)
Cites Work
- A new difference scheme for the time fractional diffusion equation
- A priori estimates for solutions of boundary value problems for fractional-order equations
- Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations
- Numerical analysis of the Burgers' equation in the presence of uncertainty
- Finite difference discretization of the Kuramoto-Sivashinsky equation
- The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
- The periodic problem for the Korteweg-de Vries equation
- Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation
- Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
- An integral equation method for the numerical solution of the Burgers equation
- The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers' equation
- A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
- Exact solutions and numerical study of time fractional Burgers' equations
- Finite difference discretization of the cubic Schrödinger equation
- A differential quadrature based numerical method for highly accurate solutions of Burgers' equation
- A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
- Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time
- An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers' equation
- Error Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier Functions
- Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
- An Energy Stable and Maximum Bound Preserving Scheme with Variable Time Steps for Time Fractional Allen--Cahn Equation
- A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem
- On two linearized difference schemes for Burgers’ equation
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Adaptive Second-Order Crank--Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models