An efficient approximation technique applied to a non-linear Lane–Emden pantograph delay differential model

The primary focus of our work is to propose a computationally effective approximation algorithm to find the numerical solution of the so-called a new design of second-order Lane–Emden pantograph delayed problem with singularity and non-linearity. Our approach based upon the novel Bessel matrix representation together with the collocation points which transforms the newly designed model problem into a non-linear fundamental matrix equation. To testify the validity and applicability of the proposed method, three test examples with non-linearity are given. The computational results are accurate as compared with the exact solutions as well as with those of numerical values reported in the literature.