广义薄膜方程的数值求解  

Numerical Solution of Generalized Thin Film Equation

作　　者：贺裕[1] 付宝君[1] 杨雨婷 HE Yu;FU Baojun;YANG Yuting(Harbin Normal University,Harbin,Heilongjiang Province,150025 China)

机构地区：[1]哈尔滨师范大学,黑龙江哈尔滨150025

出　　处：《科技创新导报》2022年第22期229-232,共4页Science and Technology Innovation Herald

基　　金：黑龙江省省属高等学校基本科研业务费科研项目(项目名称:Galerkin-再生核方法求解一类偏微分方程算法研究,项目编号:2020-KYYWF-0356);哈尔滨师范大学计算机科学与信息工程学院自然科学基金项目(项目名称:Galerkin-再生核方法求解一类偏微分方程算法研究)。

摘　　要：本文以再生核理论为基础,将再生核函数与样条函数有机结合,生成再生核样条基函数,并以基函数的线性组合构造近似解。与经典的再生核方法相比,降低了问题的复杂度,保证近似解高速的一致收敛性;与传统的样条逼近方法相比,基函数更简洁,且误差的精度大幅度提升,同时给出了算法的理论分析,方法的稳定性和有效性通过数值算例展现出来。In this paper,based on the theory of reproducing kernel,the reproducing kernel spline basis function is generated by organically combining the reproducing kernel function with the spline function,and the approximate solution is constructed by the linear combination of the basis functions.Compared with the classical reproducing kernel method,it reduces the complexity of the problem and ensures the high speed uniform convergence of the approximate solution.Compared with the traditional spline approximation method,the basis function is more con-cise and the error accuracy is greatly improved.At the same time,the theoretical analysis of the algorithm is given.The stability and effectiveness of the method are demonstrated through numerical examples.

关 键 词：四阶抛物方程 再生核空间 再生核样条函数 时间差分 

分 类 号：O175.26[理学—数学]