In this study, a novel second-order prediction differential model is designed, and numerical solutions of this novel model are presented using the integrated strength of the Adams and explicit Runge–Kutta schemes. The idea of the present study comes to the mind to see the importance of delay differential equations. For verification of the novel designed model, four different examples of the designed model are numerically solved by applying the Adams and explicit Runge–Kutta schemes. These obtained numerical results have been compared with the exact solutions of each example that indicate the performance and exactness of the designed model. Moreover, the results of the designed model have been presented numerically and graphically.

中文翻译：

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用Adams和显式Runge-Kutta数值方法求解的新型二阶预测微分模型的设计

在这项研究中，设计了一个新颖的二阶预测微分模型，并利用Adams的综合强度和显式Runge-Kutta方案给出了该新颖模型的数值解。本研究的想法浮现在脑海，以了解延迟微分方程的重要性。为了验证新颖的设计模型，通过应用Adams和显式的Runge-Kutta方案对设计模型的四个不同示例进行了数值求解。将这些获得的数值结果与每个示例的精确解决方案进行比较，这些示例表明了设计模型的性能和正确性。此外，设计模型的结果已通过数字和图形方式呈现。