An interval solution for the n-th order linear ODEs with interval initial conditions

Fahimeh Goodarzi; Mahmoud Hadizadeh; Farideh Ghoreishi

Vol. 18 No. 1 (2013)

Regular Articles

An interval solution for the n-th order linear ODEs with interval initial conditions

Fahimeh Goodarzi
Mahmoud Hadizadeh
Farideh Ghoreishi

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

Abstract

In this paper, a new method for interval solution of the $n^{th}$
order linear ordinary differential equations (ODEs) with interval
initial conditions is constructed. In this approach, by using the
Neher's algorithm \cite{ref1}, first we obtain a guaranteed
enclosure solution for an initial point value problem and then
based on the Moore's idea \cite{ref2021,ref3}, we transform this
solution to arrive at an interval solution for the main problem.
For the sake of clarity, we present an algorithm in terms of the
linear second order ODEs ($n=2$). Finally, some numerical examples
are presented to demonstrate the efficiency of the proposed
algorithm.

PDF