Three-Step Third-Derivative Block Multistep Algorithm for Solving Second-Order Nonlinear Lane–Emden-Type Differential Equations

Abstract

In this paper, a direct solution for some well-known classes of LaneEmden-type second-order nonlinear ordinary differential equations is proposed, without converting them into a first-order system of equations by using a new class of third-derivative block multistep methods. These methods were derived from a continuous scheme through an interpolation and collocation technique and are assembled in block forms to produce the numerical solution in the specified interval on the entire range of integration. The properties of the block method are discussed and the efficiency of the method is shown when applied on some second-order nonlinear LaneEmden-type differential equations. It was observed that the method was consistent, zero stable, convergent and is stable in the interval [4.4, 0]. The result shows that the method is suitable for the solution of the nonlinear LaneEmden-type equations and performs better when compared to those in the Literature.