基于谱方法和单纯形算法的一类偏微分方程参数反演研究  

Parameters Inversion Study of a Kind of Partial Differential Equation Based on Spectral Method and Nelder-Mead Simplex Algorithm

作　　者：王福昌[1] 贺财宝 WANG Fuchang;HE Caibao(Department of Basic Courses,Institute of Disaster Prevention,Sanhe 065201,China)

机构地区：[1]防灾科技学院基础部,河北三河065201

出　　处：《滨州学院学报》2024年第2期41-45,共5页Journal of Binzhou University

基　　金：河北省高等学校科学研究计划项目(ZC202112)。

摘　　要：根据观测数据反演偏微分方程参数具有重要的应用价值。通过基于快速傅立叶变换的谱方法实现对偏微分方程快速高精度求解,与观测数据结合建立待优化的目标函数,再用带边界约束的Nelder-Mead单纯形优化方法进行参数反演。通过算例证实了算法的有效性。Parameters inversion of partial differential equation from observed data has great values.Based on FFT spectral method and Nelder-Mead simplex algorithm,a practical algorithm is presented.Given the guess values of parameters,the prediction values of partial differential equations solutions can be computed by the FFT spectral algorithm,and the optimization objective function can be constructed using difference between observed data and prediction values.So,the optimal parameters and order are searched by Nelder-Mead simplex optimization method.Finally,by computer simulation,a set of feasible inversion method is presented for study scientific and engineering problems.

关 键 词：快速傅立叶变换 谱方法 Nelder-Mead单纯形法 偏微分方程 参数反演 

分 类 号：O175[理学—数学] O193[理学—基础数学]