摘要
本文提出了一种求解Caputo时间分数阶反应扩散方程的高阶数值方法。对Caputo时间分数阶导数采用L2插值逼近离散,对空间二阶导数采用中心差分离散,从而构造方程的数值离散格式;并证明了该数值格式是无条件稳定的,且收敛阶为O(τ3-α+h 2)(0<α<1);同时给出一个数值算例,验证该数值格式具有稳定性和收敛性。
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 numerical 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+h 2)(0<α<1).A numerical example is given to verify the stability and convergence of the scheme.
作者
何咏晖
陈景华
刘欣然
HE Yonghui;CHEN Jinghua;LIU Xinran(School of Sciences,Jimei University,Xiamen 361021,China;Digital Fujian Big Data Modeling and Intelligent Computing Institute,Xiamen 361021,China)
出处
《集美大学学报(自然科学版)》
2026年第2期240-252,共13页
Journal of Jimei University:Natural Science
基金
福建省自然科学基金项目(2024J01724,2024J01119)
福建省高校数学学科联盟其他高校项目(2024SXLMMS03)
数字福建大数据建模与智能计算研究所开放基金
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
fractional
reaction-diffusion equation
L2 scheme
finite difference
stability
convergence
