摘要
大量线性与非线性抛物型方程反问题以各种不同形式出现在不同应用背景下,这类方程的研究有重要的应用价值,但是非线性抛物型方程反问题存在不适定性,文中利用半中心差分法思想设计了稳定的数值算法求解反问题,研究了一类半线性抛物型方程逆时反问题的数值算法并进行数值模拟。数值模拟结果与精确解相吻合,说明了算法的有效性。
A large number of inverse problems of linear and nonlinear parabolic equations occur in different application contexts in various forms.It is extremely important to study on these equations,but inverse problems of nonlinear parabolic equations are ill-posed.This paper uses semi-discrete central difference method to design a stable numerical algorithm to solve inverse problems,studies a kind of numerical algorithm to solve inverse problems of semi-linear parabolic equations,and conducts numerical simulation. Results of numerical simulation are consistent with exact solutions,indicating that this algorithm is effective.
出处
《浙江理工大学学报（自然科学版）》
2014年第3期320-324,共5页
Journal of Zhejiang Sci-Tech University(Natural Sciences)
基金
国家自然科学基金(NSFC11071221
NSFC10561001)
浙江理工大学科研基金(KY2012015)
关键词
非线性抛物型
反问题
半中心差分
数值模拟
爆破时间
nonlinear parabolic
inverse problems
semi-discrete central difference
numerical simulation
blow up time
