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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (4): 29-39.doi: 10.6040/j.issn.1671-9352.0.2022.352

• • 上一篇    

求解非线性伪抛物方程的重心Lagrange插值配点法

屈金铮1,李金1,2*,苏晓宁1   

  1. 1.华北理工大学理学院, 河北 唐山 063210;2.河北省数据科学与应用重点实验室, 河北 唐山 063210
  • 发布日期:2023-03-27
  • 作者简介:屈金铮(1998— ),男,硕士研究生,研究方向为重心插值配点法理论、网络与信息安全. E-mail:qjz1579043951@163.com*通信作者简介:李金(1980— ),男,博士, 教授,硕士生导师,研究方向为边界元理论及其数值解、超奇异积分的数值计算和重心插值配点法理论. E-mail:lijin@ncst.edu.cn
  • 基金资助:
    河北省自然科学基金资助项目(A2019209533)

Barycentric Lagrange interpolation collocation method for solving nonlinear pseudo-parabolic equations

QU Jin-zheng1, LI Jin1,2*, SU Xiao-ning1   

  1. 1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China;
    2. Hebei Key Laboratory of Data Science and Application, Tangshan 063210, Hebei, China
  • Published:2023-03-27

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摘要： 提出了重心Lagrange插值配点法求解一类非线性伪抛物方程。首先,介绍了重心Lagrange插值并给出了微分矩阵表达式。其次,构造了求解非线性伪抛物方程的直接线性化迭代格式、部分线性化迭代格式、Newton线性化迭代格式。再次,未知函数和初边值条件利用重心Lagrange插值函数来近似,利用配点法得到离散方程,获得了方程的矩阵表达式。最后,数值算例表明,重心Lagrange插值配点法具有高精度和高效率的优点。

关键词: 非线性伪抛物方程, 重心Lagrange插值, 配点法, 迭代格式

Abstract: Barycentric Lagrange interpolation collocation method for solving a class of nonlinear pseudo-parabolic equations is proposed. Firstly, barycentric Lagrange interpolation is introduced and the expression of differential matrix is given. Secondly, direct linearized iterative scheme, partial linearized iterative scheme, Newton linearized iterative scheme for solving nonlinear pseudo-parabolic equation are constructed. Thirdly, unknown functions and initial-boundary value conditions are approximated by barycentric Lagrange interpolation function, discrete equation is obtained by using collocation method, then the matrix equation is obtained. Finally, numerical examples show that the barycentric Lagrange interpolation collocation method has the advantages of high precision and high efficiency.

Key words: nonlinear pseudo-parabolic equation, barycentric Lagrange interpolation, collocation method, iterative scheme

中图分类号: 

  • O241.82
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