Taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science

Taylor series method is applied to a class of nonlinear singular boundary value problems without requiring any specific technique in handling the singularity at the origin. For the problems with exponential nonlinearity, a variable transformation is introduced to accelerate the convergence of the solution by converting this exponential nonlinearity into a polynomial nonlinearity. The efficiency and applicability of the algorithm are assessed and tested on several problems arising in applied science. Padé approximants are used to verify that the series solutions to these problems converge within the boundaries. An error analysis is presented and the results show that the analytical approximate solutions obtained are highly accurate.