一维半线性抛物型方程反问题的数值解法  

Numerical Solution of an Inverse Problem for the One-Dimensional Semi-Linear Parabolic Equation

作　　者：王波[1,2] 邹广安[3,4] 刘霞[2] 

机构地区：[1]河南大学应用数学研究所,河南开封475004 [2]河南大学数学与信息科学学院,河南开封475004 [3]海洋环流与波动重点实验室中国科学院海洋研究所,青岛266071 [4]中国科学院大学,北京100049

出　　处：《河南大学学报（自然科学版）》2013年第6期599-604,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基金项目(40805020)

摘　　要：利用有限分差法和有限体积法针对一类带源项和未知Robin边界条件的一维半线性抛物型反问题进行数值求解.先给出一个附加条件,然后引入一个变换,将所求解的问题分成两部分分别求解.利用矩阵特征值法给出离散格式的稳定条件,最后给出数值算例,验证了该方法的有效性.In this paper, the finite difference method and finite volume method are provided for solving a one-dimensional semi-linear parabolic inverse problem with source term and unknown Robin boundary conditons. With an additonal condition and transformations, the inverse problem can be divided into two separate problems and solved respectively. According to the method of matrix-eigenvalue, the condition for the stability of the scheme is obtained. The numerical experiment will also be presented, and the numerical results illustrate that our method is effective.

关 键 词：有限差分法 有限体积法 反问题 数值试验 

分 类 号：O241[理学—计算数学]