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

作　　者：Xia Cui Guangwei Yuan Fei Zhao 

机构地区：[1]Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,P.O.Box 8009-26,Beijing 100088,China [2]College of Science,North China University of Technology,Beijing 1OO144,China [3]Graduate School of China Academy of Engineering Physics,Beijing 100088,China

出　　处：《Journal of Computational Mathematics》2021年第5期777-800,共24页计算数学（英文）

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.

摘　　要：A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is studied.The scheme is constructed with two-layer coupled discretization(TLCD)at each time step.It 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)scheme.By 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 time.Numerical tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.

关 键 词：Nonlinear diffusion problem Nonlinear two-layer coupled discrete scheme Second-order time accuracy Property analysis Unique existence CONVERGENCE 

分 类 号：O241.7[理学—计算数学]