Reprint of “Explicit exponential Runge-Kutta methods of high order for parabolic problems”. (English) Zbl 1330.65111
Editorial remark: This is a reprint of [ibid. 256, 168–179 (2014; Zbl 1314.65103)].
From the text: “A publishers’ error resulted in this article appearing in the wrong issue. The article is reprinted here for the reader’s convenience and for the continuity of the special issue. For citation purposes, please use the original publication details.”
From the text: “A publishers’ error resulted in this article appearing in the wrong issue. The article is reprinted here for the reader’s convenience and for the continuity of the special issue. For citation purposes, please use the original publication details.”
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L04 | Numerical methods for stiff equations |
Keywords:
exponential integrators; exponential Runge-Kutta methods; stiff order conditions; error bounds; semilinear parabolic problems; stiff problemsCitations:
Zbl 1314.65103References:
| [1] | Hochbruck, M.; Lubich, C.; Selhofer, H., Exponential integrators for large systems of differential equations, SIAM J. Sci. Comput., 19, 1552-1574 (1998) · Zbl 0912.65058 |
| [2] | Kassam, A.-K.; Trefethen, L. N., Fourth-order time stepping for stiff PDEs, SIAM J. Sci. Comput., 26, 1214-1233 (2005) · Zbl 1077.65105 |
| [3] | Hochbruck, M.; Ostermann, A., Exponential integrators, Acta Numer., 19, 209-286 (2010) · Zbl 1242.65109 |
| [4] | Friedli, A., Verallgemeinerte Runge-Kutta Verfahren zur Lösung steifer Differentialgleichungssysteme, (Burlirsch, R.; Grigorieff, R.; Schrödinger, J., Numerical Treatment of Differential Equations (1978), Springer: Springer Berlin), 35-50 · Zbl 0368.65039 |
| [5] | Hochbruck, M.; Ostermann, A., Explicit exponential Runge-Kutta methods for semilinear parabolic problems, SIAM J. Numer. Anal., 43, 1069-1090 (2005) · Zbl 1093.65052 |
| [7] | Dimarco, G.; Pareschi, L., Exponential Runge-Kutta methods for stiff kinetic equations, SIAM J. Numer. Anal., 49, 2057-2077 (2011) · Zbl 1298.76150 |
| [8] | Dujardin, G., Exponential Runge-Kutta methods for the Schrödinger equation, Appl. Numer. Math., 59, 1839-1857 (2009) · Zbl 1176.65109 |
| [9] | Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer: Springer New York · Zbl 0516.47023 |
| [10] | Hochbruck, M.; Ostermann, A., Exponential Runge-Kutta methods for parabolic problems, Appl. Numer. Math., 53, 323-339 (2005) · Zbl 1070.65099 |
| [11] | Henry, D., Geometric Theory of Semilinear Parabolic Equations (1981), Springer: Springer Berlin, Heidelberg · Zbl 0456.35001 |
| [12] | Butcher, J. C., On Runge-Kutta processes of high order, J. Aust. Math. Soc., 4, 179-194 (1964) · Zbl 0244.65046 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
