In this research, an approximation symbolic algorithm is suggested to obtain an approximate solution of multipantograph system of type delay differential equations (DDEs) using a combination of Laplace transform and variational iteration algorithm (VIA). The corresponding convergence results are acquired, and an efficient algorithm for choosing a feasible Lagrange multiplier is designed in the solving process. The application of the Laplace variational iteration algorithm (LVIA) for the problems is clarified. With graphics and tables, LVIA approximates to a high degree of accuracy with a few numbers of iterates. Also, computational results of the considered examples imply that LVIA is accurate, simple, and appropriate for solving a system of multipantograph delay differential equations (SMPDDEs).

中文翻译：

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使用拉普拉斯变分迭代算法求解多缩放 DDE 系统的解析计算算法

在这项研究中，提出了一种近似符号算法，以使用拉普拉斯变换和变分迭代算法（VIA）的组合来获得类型延迟微分方程（DDE）的多受电弓系统的近似解。得到相应的收敛结果，并在求解过程中设计了一种有效的选择可行拉格朗日乘子的算法。阐明了拉普拉斯变分迭代算法（LVIA）在该问题中的应用。使用图形和表格，LVIA ​​可以通过几次迭代达到很高的准确度。此外，所考虑示例的计算结果表明 LVIA ​​准确、简单且适用于求解多受电弓延迟微分方程 (SMPDDE) 系统。