ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS
作者机构：College of Mathematical SciencesYangzhou UniversityYangzhou 225002China LSECICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China COMSATS Institute of Information TechnologyLahoTePakistan McDougall School of Petroleum EngineeringThe University of TulsaTulsaOK 74104USA
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2019年第37卷第3期
页 面：297-315页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：National Natural Science Foundation of China(Grant Nos.11701502 and 11771438)
主 题：Time fractional super-diffusion equation Nonlinear system ADI schemes Stability Convergence
摘 要：As 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 *** this paper,two ADI schemes are developed for solving the two-dimensional time fractional nonlinear super-diffusion equations based on their equivalent partial integrodifferential *** 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 *** solvability,unconditional stability and L2 norm convergence of the proposed ADI schemes are proved *** 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,***,numerical experiments are carried out to support the theoretical results and demonstrate the performances of two ADI schemes.
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