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

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 [16], first we obtain a guaranteed enclosure solution for an initial point value problem and then based on the Moore's idea [7, 13], 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.