指标-3型积分代数方程的配置边值方法
Collocation Boundary Value Method for Index-3 Integral Algebraic Equations
DOI: 10.12677/pm.2024.1411396, PDF,    国家自然科学基金支持
作者: 岳 珍：贵州大学数学与统计学院，贵州 贵阳
关键词: 积分代数方程；配置边值方法；收敛阶；Integral Algebraic Equations； Collocation Boundary Value Method； Convergent Order
摘要: 针对指标-3型积分代数方程的数值解，研究其配置边值方法，基于插值多项式，利用未计算的近似值，通过将原方程进行离散化构造了指标-3型积分代数方程的配置边值方法，并分析了该方法的可解性和收敛性，证明了利用该方法求解指标-3型积分代数方程可达到较高收敛阶，最后通过数值实验验证了方法的有效性。
Abstract: Regarding the numerical solution of the index-3 integral algebraic equation, the collocation boundary value method was investigated. Based on the interpolation polynomial and the utilization of uncomputed approximate values, the collocation boundary value method for the index-3 integral algebraic equation was constructed by discretizing the original equation. The solvability and convergence of this method were analyzed. It was demonstrated that the application of this method in solving the index-3 integral algebraic equation can achieve a relatively high convergence order. Finally, the validity of the method was verified through numerical experiments.
文章引用：岳珍. 指标-3型积分代数方程的配置边值方法[J]. 理论数学, 2024, 14(11): 289-300. https://doi.org/10.12677/pm.2024.1411396

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