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

Xia Cui1, Guangwei Yuan1, Fei Zhao2,3   

  1. 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 100144, China;
    3. Graduate School of China Academy of Engineering Physics, Beijing 100088, China
  • Received:2020-03-12 Revised:2020-05-27 Published:2021-10-15
  • Supported by:
    This work is supported by the National Natural Science Foundation of China (11871112, 11971069, 11971071, U1630249), Yu Min Foundation and the Foundation of LCP. The authors would like to thank the anonymous referees for their helpful suggestions to enhance the paper.

Xia Cui, Guangwei Yuan, Fei Zhao. ANALYSIS ON A NUMERICAL SCHEME WITH SECOND-ORDER TIME ACCURACY FOR NONLINEAR DIFFUSION EQUATIONS[J]. Journal of Computational Mathematics, 2021, 39(5): 777-800.

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 space and time. Numerical tests verify the theoretical results, and illustrate its superiority over the CN and BDF2 schemes.

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