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算子矩阵法求高阶弱奇异积分微分方程数值解

DOI: 10.11830/ISSN.1000-5013.2013.05.0581

Keywords: 高阶变系数, 弱奇异积分, 积分微分方程, Legendre多项式, 算子矩阵, 数值解

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Abstract:

利用Legendre多项式的定义和性质,给出Legendre多项式微分算子矩阵,得到任意阶弱奇异积分的近似求积公式,并将原方程转换为代数方程.收敛性分析说明该方法是收敛的,数值算例验证了该方法的有效性和理论分析的正确性.

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