A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations
作者：
Highlights：
• In this paper, we present a new method for solving linear neutral delay differential equations.
• We derive and illustrate the main features of this novel approach that combines the Laplace transform method with (harmonic) Fourier series theory.
• We rely on computer algebra and numerical methods to implement the method.
• We derive an approximate formula for the location of the complex poles, which are required for computing the inverse Laplace transform.
• We include several examples where we compare the solutions generated by the standard Laplace method and the proposed Laplace-Fourier approach.
• It is shown that the Laplace-Fourier solution provides more accurate solutions than the conventional Laplace transform solution.
摘要
•In this paper, we present a new method for solving linear neutral delay differential equations.•We derive and illustrate the main features of this novel approach that combines the Laplace transform method with (harmonic) Fourier series theory.•We rely on computer algebra and numerical methods to implement the method.•We derive an approximate formula for the location of the complex poles, which are required for computing the inverse Laplace transform.•We include several examples where we compare the solutions generated by the standard Laplace method and the proposed Laplace-Fourier approach.•It is shown that the Laplace-Fourier solution provides more accurate solutions than the conventional Laplace transform solution.
论文关键词：Neutral delay differential equations,Laplace transform,Fourier series,Cauchy’s residue theorem
论文评审过程：Received 26 November 2021, Revised 24 December 2021, Accepted 30 December 2021, Available online 10 January 2022, Version of Record 10 January 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126914
