A Taylor matrix-collocation method based on residual error for solving Lane-Emden type differential equations

In this work, a new Taylor matrix method based on the collocation points and residual correction method is developed to solve the linear Lane-Emden differential equations with initial conditions. Correction of the approximate solution obtained by Taylor collocation method is performed by means of the error differential equation with the Residual function. Details of the method are presented and some numerical results along with error estimation are given to clarify the efficiency and high accuracy of the method.