This research work is related to establish a powerful algorithm for the computation of numerical solution to nonlinear variable order integro-differential equations (VO-IDEs). The adopted procedure is based on the Haar Wavelet Method (HWM) to compute the required numerical solution to the proposed problem. Further, in the considered problem, a proportional-type delay term is involved, which is also known as the pantograph equation. For a physical problem to investigate the computational purposes, we need to first ensure its existence. For this purpose, we utilize classical fixed results given by Banach and Schauder to establish the sufficient conditions for existence of at least one approximate solution to the proposed problem. Two pertinent examples are given, where the error analysis is also recorded.

这项研究工作与建立一种强大的算法来计算非线性变量阶积分微分方程 (VO-IDE) 的数值解有关。采用的程序基于 Haar 小波方法 (HWM) 来计算所提出问题所需的数值解。此外，在所考虑的问题中，涉及比例型延迟项，也称为受电弓方程。对于一个物理问题来研究计算目的，我们需要首先确保它的存在。为此，我们利用 Banach 和 Schauder 给出的经典固定结果来建立所提出问题存在至少一个近似解的充分条件。给出了两个相关的例子，其中也记录了错误分析。