An improved Bessel collocation method with a residual error function to solve a class of Lane–Emden differential equations

Abstract

In this study, the modified Bessel collocation method is presented to obtain the approximate solutions of the linear Lane–Emden differential equations. The method is based on the improvement of the Bessel polynomial solutions with the aid of the residual error function. First, the Bessel collocation method is applied to the linear Lane–Emden differential equations and thus the Bessel polynomial solutions are obtained. Second, an error problem is constructed by means of the residual error function and this error problem is solved by using the Bessel collocation method. By summing the Bessel polynomial solutions of the original problem and the error problem, we have the improved Bessel polynomial solutions. When the exact solution of the problem is not known, the absolute errors can be approximately computed by the Bessel polynomial solution of the error problem. In addition, examples that illustrate the pertinent features of the method are presented, and the results of this investigation are discussed.