A linearized finite difference scheme for time-space fractional nonlinear diffusion-wave equations with initial singularity

被引:0
|
作者
Mohmed Elmandi, Emadidin Gahalla [1 ]
Huang, Jianfei [1 ,2 ]
机构
[1] Yangzhou Univ, Coll Math Sci, Yangzhou, Jiangsu, Peoples R China
[2] Univ Khartoum, Fac Educ, POB 321, Khartoum, Sudan
基金
中国国家自然科学基金;
关键词
convergence; fractional nonlinear diffusion-wave equations; initial singularity; linearized scheme; stability; ELEMENT-METHOD; CONVOLUTION QUADRATURE; CONVECTION-DIFFUSION; APPROXIMATION; MESH;
D O I
10.1515/ijnsns-2021-0388
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper presents a linearized finite difference scheme for solving a kind of time-space fractional nonlinear diffusion-wave equations with initial singularity, where the Caputo fractional derivative in time and the Riesz fractional derivative in space are involved. First, the considered problem is equivalently transformed into its partial integro-differential form. Then, the fully discrete scheme is constructed by using the Crank-Nicolson technique, the L1 approximation, and the convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and the fractional central difference formula are applied to approximate the second-order derivative and the Riesz fractional derivative in space, respectively. Moreover, the stability and convergence of the proposed scheme are strictly proved by using the discrete energy method. Finally, some numerical experiments are presented to illustrate the theoretical results.
引用
收藏
页码:1769 / 1783
页数:15
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