Legendre谱方法求解第二类Fredholm积分方程
The Legendre Spectral Method for Numerical Solution of the Second Fredholm Integral Equation
DOI: 10.12677/AAM.2023.123107, PDF,    国家自然科学基金支持
作者: 董帅鑫：西华师范大学数学与信息学院，四川 南充；陈 冲*：西华师范大学公共数学学院，四川 南充
关键词: 第二类Fredholm积分方程；Legendre-Gauss求积公式；级数展开法；Fredholm Integral Equation of the Second Kind； Legendre-Gauss Quadrative Formula； Series Expansion Method
摘要: 本文提出了非奇异的第二类Fredholm积分方程求解的Legendre谱方法。首先作积分变换，然后应用Legendre-Gauss求积公式与级数展开法分别对积分项与未知函数做近似，再对变换后的积分方程求近似解，并进行误差分析，最后通过数值算例，验证了该方法的可行性与有效性。
Abstract: In this paper, a Legendre spectral method for solving the second Fredholm integral equation is presented. Firstly, the integral transformation is performed, and then the Legendre-Gauss quadrative formula combined with series expansion method are used to approximate the integral term and the unknown function, and then the approximate solution of the transformed integral equation is obtained, and the error analysis is carried out. Finally, the feasibility and effectiveness of the method are verified by numerical examples.
文章引用：董帅鑫, 陈冲. Legendre谱方法求解第二类Fredholm积分方程[J]. 应用数学进展, 2023, 12(3): 1054-1067. https://doi.org/10.12677/AAM.2023.123107

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