# [1]张 俊,范馨月.一类浅水波模型的数值方法[J].南京师大学报(自然科学版),2015,38(01):32. 　Zhang Jun,Fan Xinyue.Numerical Methods for a Class of Shallow Water Equation[J].Journal of Nanjing Normal University(Natural Science Edition),2015,38(01):32. 点击复制 一类浅水波模型的数值方法() 分享到： var jiathis_config = { data_track_clickback: true };

2015年01期

32

2015-06-30

## 文章信息/Info

Title:
Numerical Methods for a Class of Shallow Water Equation

(1.贵州财经大学数学与统计学院,贵州 贵阳 550025)(2.贵州大学理学院,贵州 贵阳 550025)
Author(s):
(1.School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)(2.College of Science,Guizhou University,Guiyang 550025,China)

Keywords:

O156.5

A

Abstract:
We turn to study the numerical solution of the shallow water equation. We propose two different schemes to numerically solve this equation. A detailed analysis is carried out for these schemes,and we prove that the overall schemes are unconditionally stable. The error estimation shows that the linearized Euler schema in time plus Fourier spectral method in space is convergent with the convergence order O(Δt+N1-m),and higher order convergences can be obtained if the second order backward differentiation or Crank-Nicolson schema are used to discretize the equation in time. At last,we use the proposed methods to investigate the asymptotical decay rate of the solutions to the shallow water wave equation. We equally discuss the role of the diffusion terms,the geometric dispersion and the nonlinearity respectively. The performed numerical experiment confirms that the decay rates in L2-norm,L-norm,and H1-seminorm are very close to -1/4,-1/2,and -3/4 respectively. These numerical results are consistent with the known theoretical prediction.

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