ANALYSIS ON A NUMERICAL SCHEME WITH SECOND-ORDER TIME ACCURACY FOR NONLINEAR DIFFUSION EQUATIONS

作     者：Xia Cui Guangwei Yuan Fei Zhao Xia Cui;Guangwei Yuan;Fei Zhao

作者机构：Laboratory of Computational PhysicsInstitute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China College of ScienceNorth China University of TechnologyBeijing 1OO144China Graduate School of China Academy of Engineering PhysicsBeijing 100088China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2021年第39卷第5期

页      面：777-800页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：This work is supported by the National Natural Science Foundation of China(11871112,11971069,11971071,U1630249) Yu Min Foundation and the Foundation of LCP 

主　　题：Nonlinear diffusion problem Nonlinear two-layer coupled discrete scheme Second-order time accuracy Property analysis Unique existence Convergence 

摘      要：A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is *** scheme is constructed with two-layer coupled discretization(TLCD)at each time *** does not stir numerical oscillation,while permits large time step length,and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinear schemes,the Crank-Nicolson(CN)scheme and the backward difference formula second-order(BDF2)*** developing a new reasoning technique,we overcome the difficulties caused by the coupled nonlinear discrete diffusion operators at different time layers,and prove rigorously the TLCD scheme is uniquely solvable,unconditionally stable,and has second-order convergence in both s-pace and *** tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.