Research On Numerical Solutions Of Partial Differential Equation And Partial Integro-differential Equation Based On Local Polynomial Regression

Local polynomial regression, as a nonparametric regression, nonlinear data modeling, one of thethree important methods, its theoretical framework and its application in recent20years have maderapid and extensive development. And it is widely used in nonlinear time series, communications, imageprocessing, financial and other fields. Local polynomial regression application not only abroad developsvery fast, but also gets more and more attention in China.Thesis of selected topic and introduces the relevant background, and a detailed summary of localpolynomial regression theory. Then apply binary local polynomial estimation to partial differentialequations and partial integro-differential equation numerical solution to the initial-boundary valueproblem, analyzes its numerical solution is obtained and discussed. This article is divided into four parts.It mainly study local polynomial estimation in a typical application of numerical solution of partialdifferential equation and local polynomial estimation in the application of partial integro-differentialequation numerical solution respectively.The first part, local polynomial estimation model is introduced, which discusses the origin andfeatures of local polynomial model, and discusses the problems such as the selection of modelparameters and properties.The second part, based on local polynomial theory, the numerical solution model of hyperbolicpartial differential equations is established to be solved. Moreover, combined with the numericalsmoothing image，mean square error (MSE) and mean absolute error (MAE) of the two concreteexamples, results are analyzed and discussed.The third part, based on local polynomial theory, the typical numerical solution model of partialintegro-differential equation is established to be solved. Combining with an instance, the numericalsmoothing image，mean square error (MSE) and mean absolute error (MAE) of an example, results areanalyzed and summarized.The fourth part summarizes this paper and analyzes the deficiency of this article.