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

This study aims to construct an implicit block method with three-point to tackle general
second-order ordinary differential equations (ODEs) directly. Hermite Interpolating …

A third-order fractional ordinary differential equation (FrODE) is very important in the
mathematical modelling of physical problems. Generally, the third-order ODE is solved by …

This paper proposes an implicit block method with two‐point to directly solve the fourth‐
order Initial Value Problems (IVPs). The implicit block method is derived by adopting Hermite …

In this work, a general implicit block method (GIBM) with two points for solving general fifth-
order initial value problems (IVPs) has been derived. GIBM is proposed by adopting the …

This paper presents an explicit hybrid method for direct approximation of second order
ordinary differential equations. The approach adopted in this work is by interpolation and …

A novel and efficient algorithm for the concurrent numerical solution of second, third and
fourth orders of ordinary differential equations is studied in this article. Collocation and …

Numerous critical and intricate systems from various disciplines of sciences are developed
by means of differential equations. Analytical methods are frequently complex or unfeasible …

A unique continuous three-step hybrid block method for the solution of second, third, and
fourth-order initial value problems with constant step size was proposed in this research. A …

In this work, a convergent hybrid block method (CHBM) with two off-grid points for direct
integration of first, second, and third-order initial value problems (IVPs) is proposed. The …