The Effect of Linear Operators in Periodical Solutions of Ordinary Differential Equations

Abstract

In the present paper, we investigate the influence of the choice of continuous linear operator for obtaining the approximate periodic solutions of ordinary second-order differential equations. In most of these problems, the periods are unknown, and the determination of these periods and periodic solutions is a difficult issue. So, a new computational method is proposed based on the symmetric operator, namely the reproducing kernel Hilbert space (RKHS) method to obtain the interval of these solutions. This operator, as a consequence of the symmetric inner product, is a symmetric operator and it will be used to show the influence on periodic solutions. The high efficiency of the proposed strategy is presented along with some illustrative examples which demonstrate their periodic interval dealing with the choice of an appropriate continuous linear operator.

Keywords

• reproducing kernel Hilbert space
• ordinary differential equation
• periodic solution
• interval of periodicity
• linear operator