首页|Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations

Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations

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In this paper,a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations,whose coefficients are determined according to accuracy constraints,necessary conditions of square conservation,and historical observation information under the linear supposition.As in the linear case,the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes,e.g.,the leapfrog (LF) scheme and the complete square conservation difference (CSCD)scheme that do not use historical observations in determining their coefficients,and the retrospective time integration (RTI) scheme that does not consider compatibility and square conservation.Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error (RMSE) during the first 2500 integration steps when no shock waves occur in the exact solution,while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step.It is concluded that reasonable consideration of accuracy,square conservation,and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations.

three-step difference schemenonlinearsquare conservationaccuracyhistorical observations

GONG Jing、WANG Bin、JI Zhong-Zhen

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1State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Mathematics and Physics Department, North China Electric Power University, Beijing 102206, China

State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Ministry of Science and Technology of China for the National Basic Research Program of China (973 Program

2011CB309704

2013

10.3878/j.issn.1674-2834.13.0036

大气和海洋科学快报(英文版)
中国科学院大气物理研究所

大气和海洋科学快报(英文版)

CSCD
影响因子：0.465
ISSN：1674-2834
年,卷(期)：2013.6(6)
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