An efficient variable stepsize rational method for stiff, singular and singularly perturbed problems

Abstract

In this article, a new iterative method of the rational type having fifth-order of accuracy is proposed to solve initial value problems. The method is self-starting, stable, consistent, and convergent, whereas local truncation error analysis has also been discussed. Furthermore, the method has been analyzed with a variable stepsize approach that increases performance while taking fewer steps with acceptable local errors. The method is also tested against some existing fifth-order methods having rational structure. The proposed one outperforms concerning maximum absolute error, final absolute error, average error, and norm, while CPU time computed in seconds is comparable. Furthermore, stiff, singular, and singularly perturbed problems for single and system of differential equations chosen for simulations yielded minor errors when solved with the new rational method.