In this paper, we adapt for the first time the operational matrices of Bernstein polynomials
method for solving directly a class of third-order ordinary differential equations (ODEs). This …

This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods
involving the fourth derivative of the solution for solving third-order ordinary differential …

The application of a hybrid block method to solving third order ordinary differential equations
is considered in this article. The hybrid method is developed for a set of equidistant hybrid …

The block hybrid collocation method with two off‐step points is proposed for the direct
solution of general third order ordinary differential equations. Both the main and additional …

Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order
(TDRKT3 (5)) is developed and proposed for solving a special type of third-order delay …

The main contribution of this paper is the development of direct explicit methods of Runge-
Kutta (RK) type for solving special fifth-Order Ordinary Differential Equations (ODEs). For this …

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 paper three pairs of embedded Runge–Kutta type methods for directly solving special
third order ordinary differential equations (ODEs) of the form y‴= f (x, y) denoted as RKD …

In this paper, three types of third-order partial differential equations (PDEs) are classified to
be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in …

In this paper, the classical RK integrators for solving quasi-linear (QL) ordinary differential
equations (ODEs) up to 5th-order have been generalized to solve class of 6th-order ODEs …