时间分数阶反应-扩散方程的高阶数值方法-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Higher-Order Numerical Method for Time-Fractional Reaction-Diffusion Equation

作者:: 何咏晖1; 陈景华1; 2; 刘欣然1; (1.集美大学理学院,福建厦门 361021;2.数字福建大数据建模与智能计算研究所,福建厦门 361021)

Author(s):: HE Yonghui1; CHEN Jinghua1; 2; LIU Xinran1; (1.School of Sciences,Jimei University,Xiamen 361021,China;2.Digital Fujian Big Data Modeling and Intelligent Computing Institute,Xiamen 361021,China)

Keywords:: fractional; reaction-diffusion equation; L2 scheme; finite difference; stability; convergence

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+h2)(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。

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 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+h2)(0＜α＜1).A numerical example is given to verify the stability and convergence of the scheme.