抛物型方程的小波配点解的存在惟一性

J4 ›› 2010, Vol. 45 ›› Issue (6): 65-69.

抛物型方程的小波配点解的存在惟一性

房保言¹,王志刚²,田双亮¹*,苏李君²

1.西北民族大学计算机科学与信息工程学院, 甘肃兰州 730030;
2.西安理工大学理学院, 陕西西安 710054

收稿日期:2009-09-24 出版日期:2010-06-16 发布日期:2010-06-17
通讯作者: 田双亮(1965-),男,教授,主要从事应用数学的研究. E-mail: Email: sl-tian@163.com
作者简介:房保言(1984-),女,硕士研究生,研究方向为应用数学. Email:fangbaoyan0820@126.com
基金资助:
国家民委科研基金资助项目(08XB07)

The existence and uniqueness of the solution of parabolic equations with wavelet collocation

FANG Bao-yan1, WANG Zhi-gang2, TIAN Shuang-liang1*, SU Li-jun2

1. School of Computer Science and Information Engineering, Northwest University for Nationalities,
Lanzhou 730030, Gansu, China; 2. School of Sciences, Xi′an University of Technology, Xi′an 710054, Shaanxi, China

Received:2009-09-24 Online:2010-06-16 Published:2010-06-17

摘要/Abstract

摘要：

小波配点法求解偏微分方程的研究已经有了一系列的结果,但是小波配点法解的存在惟一性仍未讨论。以抛物型方程为模型,构造了小波配点法,给出了隐格式和显格式解的存在惟一性。通过数值算例验证了该理论的可行性。

关键词: 小波配点;抛物型方程;解的存在惟一性

Abstract:

The study of the numerical solutions of PDEs with wavelet collocation has yielded a number of substantial results. However, the existence and uniqueness of the solution has not been discussed. The existence and uniqueness of the solution of parabolic equations with wavelet collocation are established and discussed, where its explicit scheme and implicit scheme are given. Also, wavelet collocation is applied to parabolic equations to examine its appropriateness.

Key words: wavelet collocation; parabolic equations; the existence and uniqueness of the solution

房保言1,王志刚2,田双亮1*,苏李君2. 抛物型方程的小波配点解的存在惟一性[J]. J4, 2010, 45(6): 65-69.

FANG Bao-yan1, WANG Zhi-gang2, TIAN Shuang-liang1*, SU Li-jun2. The existence and uniqueness of the solution of parabolic equations with wavelet collocation[J]. J4, 2010, 45(6): 65-69.

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