@article{ea114cc42d6f47e7a9894d77b90b5979,
title = "Waveform relaxation methods for functional differential systems of neutral type",
abstract = "We investigate continuous-time and discretized waveform relaxation iterations for functional differential systems of neutral type. It is demonstrated that continuous-time iterations converge linearly for neutral equations and superlinearly when the right hand side is independent of the history of the derivative of the solution. The error bounds for discretized iterations are also obtained and some implementation aspects are discussed. Numerical results are presented which indicate a potential speedup of this technique as compared with the classical approach based on discrete variable methods.",
author = "Zdzislaw Jackiewicz and M. Kwapisz and E. Lo",
note = "Funding Information: We investigate continuous-time and discretized waveform relaxation iterations for functional differential systems of neutral type. It is demonstrated that continuous-time iterations converge linearly for neutral equations and superlin-early when the right hand side is independent of the history of the derivative of the solution. The error bounds for discretized iterations are also obtained and some implementation aspects are discussed. Numerical results are presented which indicate a potential speedup of this technique as compared with the classical approach based on discrete variable methods. Q 1997 Academic Press * The work of the first author was partially supported by the National Science Foundation under Grant NSF DSM-9208048. ²The work of the second author was partially supported by Gdansk University Project BW5100-5-0062-6.",
year = "1997",
month = mar,
day = "1",
doi = "10.1006/jmaa.1997.5308",
language = "English (US)",
volume = "207",
pages = "255--285",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",
}