热传导方程的小波解法  

WAVELET SOLVING PROCESS OF HEAT-CONDUCTION EQUATION

作　　者：吴勃英[1] 邓中兴[2] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001 [2]哈尔滨理工大学应用科学学院,哈尔滨150080

出　　处：《应用数学学报》2001年第1期10-16,共7页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金;黑龙江省自然科学基金资助项目.

摘　　要：本文利用微分算子的小波表示，讨论一维热传导方程初值问题的Ｄａｕｂｅｃｈｉｅｓ小波解，给出此问题的显式离散格式．由于小波在时间和频率上的局部性，此方法特别适用于有奇异解的热传导方程，逼近精度高，而且没有发生解的振荡现象。In this paper, the initial value problem of one-dimension heat-conduction equation solved by Daubechies wavelet is discussed. The explicit discrete scheme of the above problem is given using the wavelet representation of differential operator. Because the wavelets have the time-frequency local property, the above method especially adapt to the heat-conduction equation with the singular solution, and its accuracy is high, and do not have the oscillation phenomenon.

关 键 词：热传导方程 微分算子 小波 显式离散格式 初值问题 数值解 

分 类 号：O551.3[理学—热学与物质分子运动论] O241.82[理学—物理]