一类非单调守恒性沙丘问题的拟小波解  

Quasi-wavelet solutions of a non-monotone conservation law for dune questions

作　　者：杨巍[1] 林京[1] 

机构地区：[1]合肥工业大学数学系,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2009年第6期920-923,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：文章用拟小波方法数值求解一类非线性发展方程。空间导数用拟小波数值格式离散,时间导数用四阶Runge-Kutta方法离散,非局部算子用Newton-Simpson数值积分公式离散;在对非局部算子的处理中,由于拟小波基中含有Gauss正则因子,因此数值计算中,加快了收敛速度;通过数值算例验证了其数值解不满足最大值原则。The quasi-wavelet method is used for obtaining the numerical solution of the nonlinear evolution equations. The quasi-wavelet discrete scheme is adopted to make the spatial derivatives discrete, while the fourth order Runge-Kutta method is used to make the temporal derivative discrete. The Newton-Simpson integral method is applied in order to make the nonlocal operator derivative discrete. Because the base of the quasi-wavelet includes Gauss regularizer, it expedites the convergence of the numerical solution. The numerical result verifies that the maximum principle is violated.

关 键 词：拟小波 非线性发展方程 非局部算子 RUNGE-KUTTA方法 

分 类 号：O351.2[理学—流体力学]