Abstract
Recently He et al. \cite{He2019} derived an analytical
solution of the system of Lane-Emden equations by using the Taylor
series method and computed a closed-form solution of the system of
Lane-Emden equations subject to given initial conditions. In this work,
this method is further explored and extended to a class of nonlinear
ODEs, PDEs, a system of Nonlinear ODEs and PDEs subject to certain
Initial conditions and boundary conditions. In some cases, we could find
exact solutions and if that is not possible then we compute approximate
solutions. We have compared these solutions with other existing
techniques and showed that the method is simple and superior to other
existing iterative techniques. We have also provided Mathematica codes
which user may find useful and can compute solutions as per their need.