具有非光滑解的第三类时滞Volterra积分方程的Müntz配置法
Müntz Collocation Method for the Third-Kind Volterra Integral Equations with Proportional Delays and Non-Smooth Solutions
摘要: 本文运用Müntz配置法求解具有非光滑解的第三类时滞Volterra积分方程并给出收敛性分析。首先选取合适的分数次多项式空间作为近似解空间，使得数值解更精准地逼近方程的解析解，再用带权的分数次Jacobi高斯求积公式近似积分算子得到全离散格式。其次通过理论分析给出数值格式在L∞和带权L2ωα,β,λ范数下的误差估计，最后通过数值实验验证了数值格式的谱精度。
Abstract: In this paper, the Müntz-collocation method is used to solve the third-kind Volterra integral equation with delay and the convergence analysis is given. Firstly, the proper fractional polynomial space is selected as the approximate solution space to make the numerical solution more accurately approach the analytic solution of the equation. Then, the fractional Jacobi Gaussian quadrature formula with weight is used to approximate the integral operator to get the fully discrete scheme. Secondly, the error estimations of the numerical scheme under L∞ norm and the weighted L2ωα,β,λ norm are given by theoretical analysis. Finally, the spectral accuracy of the numerical scheme is verified by numerical experiments.
文章引用：马晓华, 胡琼方. 具有非光滑解的第三类时滞Volterra积分方程的Müntz配置法[J]. 应用数学进展, 2022, 11(2): 630-640. https://doi.org/10.12677/AAM.2022.112070

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