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 …

We present two pairs of embedded Runge‐Kutta type methods for direct solution of fourth‐
order ordinary differential equations (ODEs) of the form y (iv)= f (x, y) denoted as RKFD …

This paper discusses a direct three-point implicit block multistep method for direct solution of
the general third-order initial value problems of ordinary differential equations using variable …

Kutta-Nyström (RKN) method is developed for second-order ordinary differential equations
with periodical solutions. The method has algebraic order four and phase-lag order eight at …

In this work, a phase-and amplification-fitted 5 (4) diagonally implicit pair of Runge–Kutta–
Nyström methods with four stages is developed to solve special second-order ordinary …

The Spectral Element Method (SEM) is a well-established high-order variant of the Finite
Element Method (FEM) used for dynamic problems. It can be combined with the Finite Cell …

In this work, a new pair of diagonally implicit Runge–Kutta–Nyström methods with four
stages is constructed. The proposed method has been derived to solve initial value …

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the
integration of initial-value problems for second-order ordinary differential equations …

A triangular splitting implementation of Runge–Kutta–Nyström–type Fourier collocation
methods is presented and analyzed in this paper. The proposed implementation relies on a …

In this paper, an improved trigonometrically fitted zero-dissipative explicit two-step hybrid
method with fifth algebraic order is derived. The method is applied to several problems …