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

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.