Jianfei Huang1; Yue Zhao2; Sadia Arshad4; Kuangying Li5; Yifa Tang2
Source Publication计算数学英文版
AbstractAs is known,there exist numerous alternating direction implicit(ADI)schemes for the two-dimensional linear time fractional partial differential equations(PDEs).However,if the ADI schemes for linear problems combined with local linearization techniques are applied to solve nonlinear problems,the stability and convergence of the methods are often not clear.In this paper,two ADI schemes are developed for solving the two-dimensional time fractional nonlinear super-diffusion equations based on their equivalent partial integrodifferential equations.In these two schemes,the standard second-order central difference approximation is used for the spatial discretization,and the classical first-order approximation is applied to discretize the Riemann-Liouville fractional integral in time.The solvability,unconditional stability and L2 norm convergence of the proposed ADI schemes are proved rigorously.The convergence order of the schemes is 0(τ+hx^2+hy^2),where τ is the temporal mesh size,hx and hy are spatial mesh sizes in the x and y directions,respectively.Finally,numerical experiments are carried out to support the theoretical results and demonstrate the performances of two ADI schemes.
Funding Project[National Natural Science Foundation of China]
Document Type期刊论文
Affiliation1.College of Mathematical Sciences,Yangzhou University
2.LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences
4.COMSATS Institute of Information Technology,LahoTe,Pakistan
5.McDougall School of Petroleum Engineering,The University of Tulsa,Tulsa,USA
Recommended Citation
GB/T 7714
Jianfei Huang,Yue Zhao,Sadia Arshad,et al. alternatingdirectionimplicitschemesforthetwodimensionaltimefractionalnonlinearsuperdiffusionequations[J]. 计算数学英文版,2019,037(003):297.
APA Jianfei Huang,Yue Zhao,Sadia Arshad,Kuangying Li,&Yifa Tang.(2019).alternatingdirectionimplicitschemesforthetwodimensionaltimefractionalnonlinearsuperdiffusionequations.计算数学英文版,037(003),297.
MLA Jianfei Huang,et al."alternatingdirectionimplicitschemesforthetwodimensionaltimefractionalnonlinearsuperdiffusionequations".计算数学英文版 037.003(2019):297.
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