Numerical solution of Lane-Emden pantograph delay differential equation: stability and convergence analysis

In this work, a collocation approach-based Bernstein operational matrix of differentiation method is used for obtaining the numerical solution of a class of modified Lane-Emden equation with delay in pantograph sense. The proposed numerical algorithm provides numerical solution by discretising the Lane-Emden pantograph delay differential equation into a system of algebraic equations which can be solved directly using any mathematical software. The consistency of the proposed numerical technique is verified with the convergence analysis of the proposed algorithm. The stability analysis of the model is also given using the Lyapunov function. Test examples and graphical representations of their solutions are included to illustrate the applicability and superiority of the proposed method over existing methods.