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On the discontinuous solutions of explicit neutral delay differential equations
  • َAli Davari,
  • Mohammad Maleki
َAli Davari
University of Isfahan

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Mohammad Maleki
National University of Malaysia
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This paper considers explicit neutral delay differential equations (NDDE) with piecewise continuous initial functions. We explain how the discontinuities in the solutions arise and present a perturbing scheme, in combination with an adaptive Legendre–Gauss–Radau collocation method, to deal with this type of problems computationally. The pointwise and mean convergence of the continuous solution of the perturbed NDDE to the discontinuous solution of the original NDDE are proved. Our new method for discontinuous NDDEs and the rigorous theoretical analysis provided are particularly important since explicit NDDEs have received little attention in the literature. Numerical results are given to show that the proposed method can be implemented in an efficient and accurate manner.
29 May 2022Submitted to Mathematical Methods in the Applied Sciences
30 May 2022Submission Checks Completed
30 May 2022Assigned to Editor
20 Jun 2022Reviewer(s) Assigned
14 Jan 2023Review(s) Completed, Editorial Evaluation Pending
25 Jan 2023Editorial Decision: Revise Minor
01 Mar 20231st Revision Received
02 Mar 2023Submission Checks Completed
02 Mar 2023Assigned to Editor
02 Mar 2023Review(s) Completed, Editorial Evaluation Pending
09 Mar 2023Reviewer(s) Assigned
20 Jun 2023Editorial Decision: Accept