非线性抛物型方程参数反问题数值求解的重心插值配点法  

Barycentric Interpolation Collocation Method of Numerical Solution of the Parameter Inverse Problem for Nonlinear Parabolic Equations

作　　者：闵涛[1] 郭娇 

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《应用泛函分析学报》2017年第4期345-354,共10页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金重大项目(51190093);国家自然科学基金(51679186);国家自然科学基金青年基金项目(11601418)

摘　　要：非线性抛物型方程的参数反演在工程技术领域具有重要的应用价值.但由于此类问题的非线性和不适定性,给求解带来了很大困难.本文主要利用重心插值配点法给出了求解一类非线性抛物型方程正问题的高精度数值解,在此基础上,根据某时刻在不同空间点和同一空间点在不同时刻的观测值,利用牛顿迭代正则化算法对其参数进行了反演,讨论了不同初始猜测以及数据随机扰动对该算法的影响,并给出了数值模拟,结果表明本文的方法可行且有效.The parameter inversion of nonlinear parabolic equation has important application value in the field of engineering technology, but it is difficult to solve because of its nonlinearity and ill-posedness. In this paper, we present a numerical solution of a class of nonlinear parabolic equations by using barycentric interpolation collocation method. On this basis, according to some time in the different space points and the same space observations of different time, the parameters are estimated by using the Newton iterative regularization algorithm, discussed the different initial guesses, and random data perturbation on the effect of algorithm, and gives the numerical simulation. The results show that the method is feasible and effective.

关 键 词：抛物型 重心插值 配点法 参数反演 牛顿迭代 正则化 

分 类 号：O241.82[理学—计算数学]