抛物型方程的小波配点解的存在惟一性  

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

作　　者：房保言[1] 王志刚[2] 田双亮[1] 苏李君[2] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2010年第6期65-69,共5页Journal of Shandong University(Natural Science)

基　　金：国家民委科研基金资助项目(08XB07)

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,但是其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。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 and its explicit scheme and implicit scheme are given.Also,wavelet collocation is applied to parabolic equations to examine its appropriateness.

关 键 词：小波配点 抛物型方程 解的存在惟一性 

分 类 号：O175[理学—数学]