Legendre Spectral Collocation Method for Third-Kind Volterra Integro-Differential Equations with Proportional Delays

本文提出了一种基于Legendre谱配置格式的数值方法，用于求解具有比例时滞项的第三类Volterra积分微分方程。首先，通过光滑变换，有效改善了方程解的正则性。随后，利用插值性质，通过定理和引理给出了误差分析。最后通过数值实验，验证了方案及算法的有效性。 In this paper, a numerical method based on the Legendre spectrum configuration format is proposed to solve the third-kind Volterra integral differential equations with proportional delay terms. Firstly, the regularity of the equation solution is effectively improved by smooth transformation. Subsequently, using the interpolation property, the error analysis is given by theorem and lemma. Finally, numerical experiments are carried out to verify the effectiveness of the scheme and algorithm.