The present study is related to the design of a new mathematical model based on the Lane–Emden pantograph delay differential equation. The new model is obtained by using the sense of delay differential equation and standard Lane–Emden second-order equation. For the numerical solutions of the designed model, a well-known Bernoulli collocation method is implemented. In order to check the perfection and exactness of the designed model, three different nonlinear examples have been solved by using the Bernoulli collocation scheme. Furthermore, the comparison of the numerical results obtained by the Bernoulli collocation scheme with the exact solutions is also presented. Moreover, some numerical tables and the graphs of absolute error are plotted using different values of N for all problems.

本研究与基于Lane-Emden受电弓延迟微分方程的新数学模型的设计有关。通过使用时滞微分方程和标准的Lane-Emden二阶方程来获得新模型。对于设计模型的数值解，实现了一种众所周知的伯努利搭配方法。为了检查设计模型的完美性和准确性，使用伯努利搭配方案解决了三个不同的非线性实例。此外，还将伯努利搭配方案获得的数值结果与精确解进行比较。此外，针对所有问题，使用不同的N值绘制了一些数值表和绝对误差图。