Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid

DOI10.3934/math.2021500zbMath1484.65154OpenAlexW3172025924MaRDI QIDQ2130890

Zhifang Liang, Yong Zhang, Li-Bin Liu, Xiaobing Bao

Publication date: 25 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2021500

zbMATH Keywords

initial value problemCaputo fractional derivativeadaptive gridmesh equidistribution

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12) Fractional ordinary differential equations (34A08)

Related Items

A collocation methods based on the quadratic quadrature technique for fractional differential equations ⋮ A high order numerical method for solving Caputo nonlinear fractional ordinary differential equations

Cites Work

• High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives
• Spectral collocation method for nonlinear Caputo fractional differential system
• A generalized Gronwall inequality and its application to a fractional differential equation
• An efficient collocation method for a Caputo two-point boundary value problem
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Recent applications of fractional calculus to science and engineering
• A spectral collocation method for nonlinear fractional boundary value problems with a Caputo derivative
• Collocation methods for general Caputo two-point boundary value problems
• A fitted scheme for a Caputo initial-boundary value problem
• Collocation methods for general Riemann-Liouville two-point boundary value problems
• Galerkin finite element method for nonlinear fractional differential equations
• Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator
• Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control
• Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells
• A posteriori error estimation in maximum norm for a two-point boundary value problem with a Riemann-Liouville fractional derivative
• An efficient numerical method for a Riemann-Liouville two-point boundary value problem
• Convergence analysis of a finite difference scheme for a Riemann-Liouville fractional derivative two-point boundary value problem on an adaptive grid
• Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
• Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• A posteriori error analysis for a fractional differential equation
• Error Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier Functions
• A finite difference method for a two-point boundary value problem with a Caputo fractional derivative
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

This page was built for publication: Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid