指标-3型积分代数方程的配置边值方法

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。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.

指标1-型积分代数方程的配置边值方法

通过构造配置边值方法求解指标-1型积分代数方程。利用拉格朗日插值公式,选取未计算的节点作插值节点,将原方程离散为一个线性方程组。由绕圈数以及剩余理论分析了该方法的可解性和收敛性。证明了该方法求解指标-1型积分代数方程具有较高的收敛阶,同时给出数值算例验证了我们的理论结果。