The aim of the present paper is to introduce a new numerical method for solving nonlinear Volterra integro-differential equations involving delay. We apply trapezium rule to the integral involved in the equation. Further, Daftardar-Gejji and Jafari method (DGJ) is employed to solve the implicit equation. Existence-uniqueness theorem is derived for solutions of such equations and the error and convergence analysis of the proposed method is presented. We illustrate efficacy of the newly proposed method by constructing examples.

中文翻译：

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求解涉及延迟的 Volterra 积分微分方程：一种新的高阶数值方法

本文的目的是介绍一种新的数值方法来求解涉及延迟的非线性 Volterra 积分微分方程。我们将梯形规则应用于方程中涉及的积分。此外，采用 Daftardar-Gejji 和 Jafari 方法 (DGJ) 求解隐式方程。导出了此类方程解的存在唯一性定理，并给出了所提出方法的误差和收敛性分析。我们通过构建示例来说明新提出的方法的有效性。