一维抛物型方程参数识别反问题的数值解法

A Numerical Solution to Parameter Identification Inverse Problems for One-Dimension Parabolic Partial Differential Equations

以函数逼近和Tikhonov正则化为基础,利用算子识别摄动法和线性化技术提出求解一维抛物型偏微分方程参数识别反问题的迭代算法,拓宽了求解此类反问题泛定方程和初边值条件的适用范围。数值模拟的结果表明,用此迭代法求解参数识别反问题具有数值精度高、稳定性好、收敛速度快的特点。

With the function approximation and Tikhonov regularization as the base,this paper presents a new type of iterative algorithm to solve inverse problems of parameter identification for onedimension parabolic partial differential equations.Using operator identification perturbation method and linear technique whereby enlarging the applicable range of partial differential equations and initialboundary values for these inverse problems. The results of numerical simulation illustrate that the iterative algorithm to solve the inverse problems of parameter identification is characterized by high accuracy in numerical values,good stability and fast convergence rate.