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 propose sixth-order two-derivative improved Runge-Kutta type methods
adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a …

This paper presents two important contributions to the field of numerical analysis for third-
order ordinary differential equations (ODEs). First, a new class of direct implicit Runge-Kutta …

The present paper aims at providing an insight to embedded Runge-Kutta sixth order
(RKSD) ordinary differential equation method for solving the initial value problem of order six …

This research work considers derivation of three step four point optimized hybrid block
method for solving general third order differential equations (odes) without reduction to …

This work involves development of an optimum third ordersingle-step explicit method for
Cauchy problems. The proposed methodis analyzed for consistency, stability, local and …

A numerical method is proposed in this paper to directly solve third order boundary value
problems that could be coupled with second order boundary value problem (s). The …

This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods
adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a …

We develop a class of continuous modified multistep methods (CMMMs) which were use as
boundary value methods for the numerical integration of special third order boundary value …

We develop a class of block unification multi-step method (BUMM) which are used as
boundary value methods for the numerical integration of third order boundary value …