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Analysis of an adaptive collocation solution for retarded and neutral delay systems

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Abstract

This paper introduces an adaptive collocation method to solve retarded and neutral delay differential equations (RDDEs and NDDEs) with constant or time-dependent delays. The delays are allowed to be small or become vanishing during the integration. We determine the convergence properties of the proposed method for neutral equations with solutions in appropriate Sobolev spaces. It is shown that the proposed scheme enjoys the spectral accuracy. Numerical results show that the proposed method can be implemented in an efficient and accurate manner for a wide range of RDDE and NDDE model problems.

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Acknowledgments

The authors are grateful to the reviewers for the constructive comments.

Funding

This work received financial support from Iran National Science Foundation through grant number 96009104.

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  1. Department of Mathematics, University of Khansar, Khansar, Iran

    Mohammad Maleki & Ali Davari

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  1. Mohammad Maleki
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  2. Ali Davari
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Correspondence to Mohammad Maleki.

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Maleki, M., Davari, A. Analysis of an adaptive collocation solution for retarded and neutral delay systems. Numer Algor 88, 67–91 (2021). https://doi.org/10.1007/s11075-020-01030-4

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