Analysis of Delay Differential Equations Using the Offset Linear Canonical Transform

Abstract

Motivated by the work of Ohira and the advantages of the offset linear canonical transform (OLCT) over the Fourier transform (FT), this paper proposes an OLCT based framework for solving a class of delay differential equations. By exploiting the operational properties of the OLCT, the original delay differ- ential equation is transformed into a Volterra-type delay integral equation in the transform domain and solved numerically using Brunners method of steps . An explicit analytical solution is derived for a special case to investigate the effect of the delay parameter. A unified transform-domain formulation is also established by relating the proposed OLCT approach to its Fourier transform counterpart. Numerical and graphical results demonstrate the accuracy and effectiveness of the proposed method and validate it through comparisons with the Fourier transform based formulation of Ohira . The proposed framework may provide a promising foundation for solving non linear delay differential equations involving transcendental terms, as both the OLCT and the resulting Volterra integral equation possess the essential properties required to handle non linearities and transcendental terms.