A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

A general analysis of accuracy and linear stability of Runge–Kutta–Nyström (RKN) methods
for solving second-order stiff problems is carried out. This analysis reveals that when …

In this paper, we develop a new collocation method for solving initial value problems of
second order ODEs. We approximate the solutions by the Legendre–Gauss interpolation …

We consider a family of half‐implicit Numerov‐type methods for the numerical solution of the
problem y′′= f (x, y). These methods use off‐step points and waste four function …

In this research, we provide a novel approach to the development of effective numerical
algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory …

In this study, a trigonometrically adapted 6 (4) explicit Runge–Kutta–Nyström (RKN) pair with
six stages is formulated, considering a previous method developed by El‐Mikkawy and …

Evolutionary techniques are used for the derivation of a six-stage sixth-order singly
diagonally implicit Runge–Kutta–Nyström (SDIRKN) method for the integration of second …

In this paper an optimization of the non-FSAL embedded RKN 6 (4) pair with six stages of
Moawwad El-Mikkawy, El-Desouky Rahmo is presented. The new method is derived after …

This research introduces a fresh methodology for creating efficient numerical algorithms to
solve first-order Initial Value Problems (IVPs). The study delves into the theoretical …

New symmetric DIRK methods specially adapted to the numerical integration of first-order
stiff ODE systems with periodic solutions are obtained. Our interest is focused on the …