A novel numerical approach and stability analysis for a class of pantograph delay differential equation

The goal of this research is to introduce a numerical technique based on shifted Chebyshev polynomial and collocation method for a second order non-linear Lane-Emden pantograph delay differential equation (PDDE) subject to initial conditions. The proposed formulation is based on converting the initial value problem (IVP) into an equivalent fundamental algebraic equation which reduces computational expense. The convergence analysis of the proposed numerical technique demonstrates the efficiency of the proposed scheme. The uniqueness and existence, regularity and stability analysis of the Lane-Emden PDDE is discussed and investigated thoroughly by providing sufficient theorems. Due to the non-availability of abundant literature, the new approach is implemented and tested against existing approaches on standard and newly constructed nonlinear examples. The comparison demonstrates that the proposed method is more accurate and consumes lesser CPU time to compute the results than the existing methods.