caa a22 4500 378860178 CHVBK 20180305123344.0 cr unu---uuuuu 161128s2003 xx s 000 0 eng 10.2478/cmam-2003-0008 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0008 A Parallel High-accuracy Method for the First-order Evolution Equation in Hilbert and Banach Spaces [Elektronische Daten] We have developed a discretization method of an arbitrarily given order of accuracy with respect to the time discretization parameter for the first-order evolution differential equation in Banach space. The method includes two levels of parallelism: the operator exponential needed for the calculation of the evolution operator can be computed in parallel (inner parallelism) and then we can compute in parallel the evolution operator at various points of the time mesh (outer parallelism). This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. first-order evolution equation nationallicence Hilbert and Banach spaces nationallicence evolution operator nationallicence error analysis nationallicence parallel high-accuracy method nationallicence stability estimates nationallicence strongly P-positive operator nationallicence Garvrilyuk Ivan P. Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, 99817 Eisenach, Germany. Makarov Vladimir L. Institute of Mathematics, National Academy of Sciences, 3 Tereschenkivska Str, 01601 Kiev, Ukraine. Ryabichev Vyacheslav L. National Taras Shevchenko University of Kyiv, Institute of Journalism, 36/1 Melnikova Str, 254119 Kiev-119, Ukraine. Computational Methods in Applied Mathematics De Gruyter 3/1(2003), 86-115 1609-4840 3:1<86 2003 3 cmam https://doi.org/10.2478/cmam-2003-0008 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2003-0008 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Garvrilyuk Ivan P. Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, 99817 Eisenach, Germany NATIONALLICENCE 700 1- Makarov Vladimir L. Institute of Mathematics, National Academy of Sciences, 3 Tereschenkivska Str, 01601 Kiev, Ukraine NATIONALLICENCE 700 1- Ryabichev Vyacheslav L. National Taras Shevchenko University of Kyiv, Institute of Journalism, 36/1 Melnikova Str, 254119 Kiev-119, Ukraine NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 3/1(2003), 86-115 1609-4840 3:1<86 2003 3 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter