二维扩散方程的区间拟小波数值解  

Study of two-dimensional diffusion equation by interval quasi-wavelet method

作　　者：曹小琴[1] 林京[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2010年第6期951-954,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：求解二维扩散方程的数值方法中,拟小波方法的精度虽然比Boltzmann方法高,但是前者的运算量比后者大很多。文章采取区间拟Shannon尺度函数为权函数,利用小波配点法对空间域离散得到对时间的常微分方程组,然后用高效的精细积分法求解,改进了拟小波方法;新方法在保证高精度的同时,使得计算量低于拟小波方法;数值实验的分析和结果证明了新方法的有效性。In view of the numerical methods for solving two-dimensional diffusion equations, the preci- sion gained by the quasi-wavelet method is higher than that by Boltzmann method, but the computa- tion of the former is much more than the latter. The interval quasi-Shannon scaling function is select- ed as weight function in this paper and the spatial domain is discretized by the wavelet collocation method. Then the system of ordinary differential equation is built and the solution of it is gained by the high-efficient precise integration method. The new approach improves the quasi-wavelet method. Compared with the quasi-wavelet method, the new approach reduces the computation while high preci- sion is kept. Finally the effect of the new approach is demonstrated by the results of numerical exampies.

关 键 词：二维扩散方程 区间拟小波法 小波配点法 精细积分法 

分 类 号：O241.82[理学—计算数学]