基于差分方法的逆时热传导问题数值方法的研究.pdf

中文摘要中文摘要本文研究了二维逆时热传导问题,即由介质在某一时刻T>O的温度场分布,(z),首先该问题不是对任意给定的函数,(z),初始温度场的数据对t=T的温度场不具有连续依赖性,. ,构造了一个基于差分方法和4阶Runge-Kutta法的解二维热传导方程正问题的数值方法,,在对逆问题使用了正则化后,应用SOR迭代求解该方程,. 关键词:逆热传导问题;不适定性;正则化;差分; SOR迭代 Abstract The砸m ofthispaper is topresent an im,ersionscheme heat problem ofdetermining theinitialtemperature distribution from itsfinalmeasur争 ment given atsome timer> are twD characters , does not eXist solution on any given function f(x). Second,the data of itsjni. tlaltemperature does not haⅣecontinuous d印endence on thetemperature 6eldof t= istosay theproblem :we need todiscuss the numerical method for thestability ofappro面mate paper isbased on regularizing method and SOR iteration tosolve thisproblem. The paper anized ohapter 1,we introduce thebasicknowl. edge ofthe i11、rer8eproblem. Inchapter 2:we give the related propeny and reg. ularizing chapter 3;we give the mathematical model fordirectheat probIem,and construct a putational algorithm which based on thedi妇fer- ence scheme for thespatialdiscretization:and thefourth—-Kutta scheme forthetemporal discretization,then the error analysis is811so百veln,In chapter we introduce themathematical model of problem,aRer regularizing thei愀problem,啪u8e theSOR iteration tosolvethisequation, thenumeric甜results of our regularized inver8ion are aLl80pre8ented. Keywords: imrel鼬heat conduction problem;ill-posed;regularization;di丑ference; SOR itera七ion II—,除了文中特别加以标注和致谢的地方外,论文中不包含其他人已经发表或撰写过的研究成果,也不包含为获得黑龙江大学或其他教育机构的学位或证书而使用过的材料. 学位论文作者答名:弓弦黜有签字日期囊翻降j明≥f日学位论文版权使用授权书本人完全了解黑龙江大学有关保留,使用学位论文的规定,同意学校保留并向国家有关部门或机构送交论文的复印件和电子版,允许论