数学季刊 ›› 2025, Vol. 40 ›› Issue (3): 295-303.doi: 10.13371/j.cnki.chin.q.j.m.2025.03.005

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变系数常微分方程边值问题的数值方法

  

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China
  • 收稿日期:2025-07-16 出版日期:2025-09-30 发布日期:2025-09-30
  • 作者简介:ZHAO Ting-ting (1998- ), female, native of Luoyang, Henan, master student of Henan University of Science and Technology, mainly engages in research on numerical solutions of differential equations; CAI Wei-yun (1982-), female, native of Xingyang, Henan, lecturer of Henan University of Science and Technology, mainly engages in computational mathematics.

Numerical Methods for Boundary Value Problems in Variable Coefficient Ordinary Differential Equations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China
  • Received:2025-07-16 Online:2025-09-30 Published:2025-09-30
  • About author:ZHAO Ting-ting (1998- ), female, native of Luoyang, Henan, master student of Henan University of Science and Technology, mainly engages in research on numerical solutions of differential equations; CAI Wei-yun (1982-), female, native of Xingyang, Henan, lecturer of Henan University of Science and Technology, mainly engages in computational mathematics.

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摘要： In order to solve the problem of the variable coefficient ordinary differential equation on the bounded domain, the Lagrange interpolation method is used to approximate the exact solution of the equation, and the error between the numerical solution and the exact solution is obtained, and then compared with the error formed by the difference method, it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.

关键词: Variable coefficient ordinary differential equations, Lagrange interpolation,  , Difference methods

Abstract: In order to solve the problem of the variable coefficient ordinary differential equation on the bounded domain, the Lagrange interpolation method is used to approximate the exact solution of the equation, and the error between the numerical solution and the exact solution is obtained, and then compared with the error formed by the difference method, it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.

Key words: Variable coefficient ordinary differential equations, Lagrange interpolation,  , Difference methods

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