Abstract
The present study aims to design a mathematical system based on the Lane–Emden third-order pantograph differential model by using the general forms of the pantograph as well as the Lane–Emden models. The designed model is divided into two types along with the various singularity details at each point. The shape factors and the pantograph points are discussed for each type of the newly designed nonlinear third-order pantograph differential model. The Bernoulli collocation scheme is implemented to find the numerical results of the novel model. To show the reliability of the designed novel nonlinear model, four different variants have been solved. Moreover, the comparison of the obtained results with the exact solutions is presented to check the accuracy of the designed novel model.