The construction of modified two‐step hybrid methods for the numerical solution of second‐
order initial value problems with periodic or oscillatory behavior is considered. The …

This paper deals with the development, analysis and implementation of an optimized hybrid
block method having different features, for integrating numerically initial value ordinary …

In this article, a third derivative continuous 2-step block Falkner-type method for the general
solution of second order boundary value problems of ordinary differential equations (ODEs) …

[EN] An optimized two-step hybrid block method is presented for integrating general second
order initial value problems numerically. The method considers two intra-step points which …

For the approximate solution of the Kepler equations and some related problems, a fourth-
order convergent functionally-fitted block hybrid Falkner method which is based on the …

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 …

This paper is devoted to the development and analysis of a modified family of Falkner-type
methods for solving differential systems of second-order initial-value problems. The …

One of the well-known schemes for the direct numerical integration of second-order initial-
value problems is due to Falkner. This paper focuses on the construction of a family of …

Recently, direct methods that involve higher derivatives to numerically approximate higher
order initial value problems (IVPs) have been explored, which aim to construct numerical …

In this article, we have considered an adaptive step-size formulation of an optimized block
method for directly solving general second-order initial value problems of ODEs numerically …