Efficient k-Derivative Methods for Lane-Emden Equations and Related Stiff Problems

Lane-Emden equations are one of singular classes of problems in mathematical physics. Existing methods for this class of problems are series and analytical methods. This study focuses on the exploration of the possibility of a class of multi-derivative methods for approximating its solution. Taylor’s series expansion was applied on a new multi-derivative backward differenti ation formula to obtain a new class of k-step, k-derivative method containing one super-future point evaluation. The k-derivative methods were applied to singular Lane-Emden Equations and related stiff equations. Matlab codes were written for the solution of problems considered and the results obtained showed the competitive strength of these methods with other methods. The methods developed have good sta bility properties, a high degree of accuracy and are effective.