非线性奇异积分方程离散方程的一个混沌现象
A Chaotic Phenomenon in Discrete Equations of Nonlinear Singular Integral Equations
DOI: 10.12677/AAM.2022.111004, PDF,    科研立项经费支持
作者: 梁 萍, 刘 华：天津职业技术师范大学理学院，天津；陈 娟：天津中德应用技术大学，天津；王 宇：上海立信会计金融学院，上海
关键词: 非线性奇异积分方程；Lagrange插值；混沌现象；Nonlinear Singular Integral Equation； Lagrange Interpolation； Chaotic Phenomenon
摘要: 本文讨论一种非常系数的非线性奇异积分方程的特征方程的数值求解。先通过对核函数做Lagrange插值，再用奇异积分的HG求积公式对积分进行离散，从而得到原方程的离散方程。再对这个非线性的离散代数方程用迭代方法求解，探讨求解过程中出现的混沌现象。
Abstract: This paper deals with the numerical solution of the characteristic equation of a nonlinear singular integral equation with extraordinary coefficients. Firstly, the kernel function is interpolated by Lagrange, and then the integral is discretized by the HG quadrature formula of singular integral, so as to obtain the discrete equation of the original equation. Then the nonlinear discrete algebraic equation is solved by iterative method, and the chaotic phenomenon in the solution process is discussed.
文章引用：梁萍, 陈娟, 刘华, 王宇. 非线性奇异积分方程离散方程的一个混沌现象[J]. 应用数学进展, 2022, 11(1): 22-27. https://doi.org/10.12677/AAM.2022.111004

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