Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation

doi:10.3390/fractalfract6080438

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	Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation
	Nong, Lijuan 1; Yi, Qian 1; Cao, Jianxiong 2; Chen, An 3
刊名	FRACTAL AND FRACTIONAL
	2022-08-01
卷号	6 期号:8
关键词	time-fractional Cattaneo equation compact difference operator L2-1(sigma) method fast discrete Sine transform sum of exponentials
DOI	10.3390/fractalfract6080438
英文摘要	The time-fractional Cattaneo equation is an equation where the fractional order alpha is an element of(1,2) has the capacity to model the anomalous dynamics of physical diffusion processes. In this paper, we consider an efficient scheme for solving such an equation in two space dimensions. First, we obtain the space's semi-discrete numerical scheme by using the compact difference operator in the spatial direction. Then, the semi-discrete scheme is converted to a low-order system by means of order reduction, and the fully discrete compact difference scheme is presented by applying the L2-1(sigma) formula. To improve the computational efficiency, we adopt the fast discrete Sine transform and sum-of-exponentials techniques for the compact difference operator and L2-1(sigma) difference operator, respectively, and derive the improved scheme with fast computations in both time and space. That aside, we also consider the graded meshes in the time direction to efficiently handle the weak singularity of the solution at the initial time. The stability and convergence of the numerical scheme under the uniform meshes are rigorously proven, and it is shown that the scheme has second-order and fourth-order accuracy in time and in space, respectively. Finally, numerical examples with high-dimensional problems are demonstrated to verify the accuracy and computational efficiency of the derived scheme.
WOS研究方向	Mathematics
语种	英语
出版者	MDPI
WOS记录号	WOS:000845956600001
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/159844]
专题	理学院
作者单位	1.Guangxi Normal Univ, Coll Math & Stat, Guilin 541004, Peoples R China; 2.Lanzhou Univ Technol, Coll Sci, Lanzhou 730050, Peoples R China; 3.Guilin Univ Technol, Coll Sci, Guilin 541004, Peoples R China
推荐引用方式 GB/T 7714	Nong, Lijuan,Yi, Qian,Cao, Jianxiong,et al. Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation[J]. FRACTAL AND FRACTIONAL,2022,6(8).
APA	Nong, Lijuan,Yi, Qian,Cao, Jianxiong,&Chen, An.(2022).Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation.FRACTAL AND FRACTIONAL,6(8).
MLA	Nong, Lijuan,et al."Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation".FRACTAL AND FRACTIONAL 6.8(2022).