Original scientific paper
An interval solution for the n-th order linear ODEs with interval initial conditions
Fahimeh Goodarzi
; Department of Mathematics, Faculty of Science, K. N.Toosi University of Technology, Tehran, Iran
Mahmoud Hadizadeh
; Department of Mathematics, Faculty of Science, K. N.Toosi University of Technology, Tehran, Iran
Farideh Ghoreishi
; Department of Mathematics, Faculty of Science, K. N.Toosi University of Technology, Tehran, Iran
Abstract
In this paper, a new method for interval solution of the 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.
Keywords
interval method; linear $n^{th}$ order ordinary differential equations; interval initial value problem; verified solution; guaranteed error bound
Hrčak ID:
101485
URI
Publication date:
10.5.2013.
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