小波方法解对流方程中的压缩存储和快速算法

The Compacting Memory and Fast Algorithm of Wavelets for Solving Convection Equations

采用有限支集正交小波数值求解线性对流方程的奇性传播问题．提出将传播矩阵按放缩尺度分块，研究了子块元素所具有的某种平移不变性和放缩相似性，在此基础上提出一种压缩存储方法和快速算法，效果显著．对多方面发挥小波方法特长问题还作了进一步的讨论，最后给出了一个数值例子．

A numerical method of orthogonal wavelets with a finite subset is used to solve the propagation of singularity of linear convection equations. It is proposed that the transition matrices are to be partitioned according to the enlargement contraction scales. The translation invariability and the enlargement contraction similarity of the elements in the blockette are investigated. Algorithms for the compacting memory and fast calculation of the transition matrix are presented and are found very satisfactory. The exploitation of the advantages of wavelets in solving P. D. E. is also discussed and a numerical example is given.