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 …

In this paper, we propose a simple approach to the construction of a general class of L-
stable explicit second-order one-step methods for solving stiff problems. These methods are …

Solving stiff, singular, and singularly perturbed initial value problems (IVPs) has always
been challenging for researchers working in different fields of science and engineering. In …

Singular problems with discontinuities or steep gradients challenge traditional numerical
integration methods. This study introduces the Rational Multi-Derivative Integrator (RMDI) …

There exists initial value problem whose solution possesses singularity. Studies show that
conventional numerical method such as multistep method fail woefully near the singular …

In this study, a new class of exponential-rational methods (ERMs) for the numerical solution
of first order initial value problems has been developed. Developments of third order and …

This paper considers extrapolation of rational methods for the numerical solution of initial
value problems (IVPs) in ordinary differential equations (ODEs). The extrapolation code …

In this paper, a class of rational methods of second to fourth order of accuracy are presented.
The methods are developed by considering the concept of the closest points of …

Exponentially-fitted numerical methods are appealing because L-stability is guaranteed
when solving initial value problems of the form Such numerical methods also yield the exact …

In this study, the concept of block methods based on rational approximants is introduced for
the numerical solution of first order initial value problems. These numerical methods are also …