摘要
本文提出了求解时间分数阶对流扩散方程两种高效数值算法。首先基于Laplace变换及指数变换将原问题转化为整数阶扩散问题;然后采用Crank-Nicolson格式并分别结合二阶中心差分和四阶紧致差分方法,设计出两种求解时间分数阶对流扩散方程的高精度差分格式,并利用Fourier方法证明两种差分格式都是稳定的。数值实验验证了两种格式的有效性。
This paper proposes two efficient numerical algorithms for solving the time fractional convection-diffusion equation. First, the original problem is transformed into an integer-order diffusion problem based on Laplace transform and exponential transform. Then, using Crank-Nicolson format and combining second order central difference and fourth order compact difference respectively, two kinds of high precision difference formats for solving time fractional order convection-diffusion equations are designed, and both schemes are proved to be stable by using Fourier method. Numerical experiments verify the effectiveness of the two formats.
出处
《应用数学进展》
2020年第10期1701-1709,共9页
Advances in Applied Mathematics
关键词
时间分数阶对流扩散方程
LAPLACE变换
指数变换
二阶中心差分格式
四阶紧致差分格式
Time Fractional Order Convection-Diffusion Equation
Laplace Transform
Exponential Transformation
Second Order Central Difference Scheme
Fourth Order Compact Difference Scheme