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\begin{document}

\title{On the discontinuous solutions of explicit neutral delay differential
equations}



\author[1]{َAli Davari}%
\author[2]{Mohammad Maleki}%
\affil[1]{University of Isfahan}%
\affil[2]{National University of Malaysia}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
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.%
\end{abstract}%



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\textbf{Hosted file}

\verb`On the discontinuous solutions of explicit neutral delay differential equations.rar`  available at \url{https://authorea.com/users/485889/articles/571102-on-the-discontinuous-solutions-of-explicit-neutral-delay-differential-equations}

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