集美大学学报（自然科学版）2026，Vol.31Issue(2)：240-252,13.DOI:10.19715/j.jmuzr.2026.02.11
时间分数阶反应-扩散方程的高阶数值方法
Higher-Order Numerical Method for Time-Fractional Reaction-Diffusion Equation
摘要
Abstract
In this paper,a high order numerical method for solving time-fractional diffusion equations is presented.The time-fractional derivative of Caputo is discretized using the L2 interpolation approximation,and the second-order spatial derivative is discretized by the central difference scheme,thus constructing the numer-ical discrete scheme for the equation.It is proved that the numerical scheme is unconditionally stable and has a second-order convergence rate O(τ3-α+h2)(0＜α＜1).A numerical example is given to verify the stability and convergence of the scheme.关键词
分数阶/反应-扩散方程/L2格式/有限差分/稳定性/收敛性Key words
fractional/reaction-diffusion equation/L2 scheme/finite difference/stability/convergence分类
数理科学引用本文复制引用
何咏晖,陈景华,刘欣然..时间分数阶反应-扩散方程的高阶数值方法[J].集美大学学报（自然科学版）,2026,31(2):240-252,13.基金项目
福建省自然科学基金项目(2024J01724,2024J01119) （2024J01724,2024J01119）
福建省高校数学学科联盟其他高校项目(2024SXLMMS03) （2024SXLMMS03）
数字福建大数据建模与智能计算研究所开放基金 （）
