发表机构
SRM University AP（SRM大学安得拉邦校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于偏移线性正则变换的框架求解延迟微分方程，转化为Volterra积分方程并用步进法数值求解，推导解析解并验证有效性，为非线性延迟方程提供基础。
AI 中文摘要
受Ohira工作的启发以及偏移线性正则变换（OLCT）相对于傅里叶变换（FT）的优势，本文提出了一种基于OLCT的框架来求解一类延迟微分方程。通过利用OLCT的运算性质，原始延迟微分方程在变换域中被转化为Volterra型延迟积分方程，并使用Brunners步进法进行数值求解。针对一个特殊情况推导出了显式解析解，以研究延迟参数的影响。通过将所提出的OLCT方法与傅里叶变换对应方法相关联，还建立了一个统一的变换域公式。数值和图形结果证明了所提方法的准确性和有效性，并通过与基于傅里叶变换的Ohira公式进行比较来验证。所提出的框架可能为求解涉及超越项的非线性延迟微分方程提供有前景的基础，因为OLCT和所得的Volterra积分方程都具备处理非线性和超越项所必需的基本性质。
英文摘要
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.
