Diagonally implicit Runge-Kutta formulae for the numerical integration of nonlinear two-point boundary value problems
type: Item
instance of: scholarly article
title: Diagonally implicit Runge-Kutta formulae for the numerical integration of nonlinear two-point boundary value problems
zbMATH Open document ID: 0565.34012
DOI: 10.1016/0898-1221(84)90043-9
publication date: 1984-01-01T00:00:00Z
review text: This paper considers the standard implicit Runge Kutta formulae for solving a system of equations of the form (1) (d/dt)\b{y}\(=\underline f(t,\underline y)\) with (2) g(\b{y}(a),\b{y}(b))\(=0\). The fully implicit Runge Kutta formulae lead to a set of non-linear equations. These can be simplified using the diagonally implicit Runge Kutta formula which reduces the difficulty in the algebra. However non-linear equations are still produced which incorporate (2). A special example of the simplifications is considered using the implicit mid-point rule and separated boundary conditions. Numerical results are obtained for several well-known systems. Although the analysis is applicable to both separated and non-separated boundary conditions only the former appear in the numerical examples. The main purpose of this paper is the derivation of an efficient class of Runge-Kutta formulae for two point boundary value problems and estimates of the number of operations involved in the algorithms are given.
Mathematics Subject Classification ID: 65J99
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L99
zbMATH DE Number: 3901180
zbMATH Keywords: Runge Kutta formulae
zbMATH Keywords: mid-point rule
zbMATH Keywords: Numerical results
zbMATH Keywords: algorithms
author: Jeff R. Cash
reviewed by: Brian L. Burrows
MaRDI profile type: Publication
full work available at URL: 0898-1221(84)90043-9
OpenAlex ID: W1998010299
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3901180