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

作者：Goodarzi Fahimeh; Hadizadeh Mahmoud^*; Ghoreishi Farideh

来源：Mathematical Communications, 2013, 18(1): 257-270.

• interval method
• linear n(th) order ordinary differential equations
• interval initial value problem
• verified solution
• guaranteed error bound

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.

• 出版日期2013-5