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 …

Over the years, researches have shown that fixed (constant) step-size methods have been
efficient in integrating a stiff differential system. It has however been observed that for some …

In this paper, the implementation of second derivative general linear methods (SGLMs) in a
variable stepsize environment using Nordsieck technique is discussed and various …

Abstract General Linear Methods (GLMs) were introduced as the natural generalizations of
the classical Runge–Kutta and linear multistep methods. An extension of GLMs, so-called …

Second derivative diagonally implicit multistage integration methods (SDIMSIMs) as a
subclass of second derivative general linear methods (SGLMs) have been divided into four …

It is the purpose of this paper to study the construction and implementation of Nordsieck
second derivative methods for the numerical integration of stiff systems of first order ordinary …

An extension of general linear methods (GLMs), so-called SGLMs (GLMs with second
derivative), was introduced to the case in which second derivatives, as well as first …

Abstract Theory of general linear methods (GLMs) for the numerical solution of autonomous
system of ordinary differential equations of the form y′= f (y) is extended to include the …

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 …

The Adams-type second derivative multistep methods of WH Enright is generalized to a
class of boundary value methods for the numerical solution of initial value problems in …