In this paper, we have a zeal for fulfilling the estimated scientific answers for the calculus of variations by using the Sumudu transform method (STM). The main target is to search the numerical arrangement of ordinary differential equations (ODEs) which emerge from the variational problems where first the fundamental condition for the arrangement of the issue is to fulfill the Euler–Lagrange condition and then solve the equations using STM. The valuable properties of the Sumudu change technique are used to downsize the calculation of the issue to a gathering of straight arithmetical conditions. We introduce four variational problems and discover the numerical solution of those problems using STM and plot the curves of those solutions. These models are picked such that there exist systematic answers for them to offer a reasonable diagram and show the effectiveness of the proposed strategy. Numerical outcomes are registered utilizing Maple programming.

中文翻译：

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求解等周变分问题的数值求解技术

在本文中，我们热衷于通过使用 Sumudu 变换方法 (STM) 来实现变分法的估计科学答案。主要目标是搜索从变分问题中出现的常微分方程 (ODE) 的数值排列，其中问题排列的基本条件是满足欧拉-拉格朗日条件，然后使用 STM 求解方程。Sumudu 变化技术的宝贵特性用于将问题的计算缩小为直接算术条件的集合。我们引入了四个变分问题，并使用 STM 发现了这些问题的数值解，并绘制了这些解的曲线。选择这些模型，以便为它们提供系统的答案，以提供合理的图表并显示所提出策略的有效性。使用 Maple 编程记录数值结果。