Fourth Order Partitioned Methods Designed for the Time Integration of Atmospheric Models
Artikel i vetenskaplig tidskrift, 2023

In this paper we derive a fourth order two step Runge-Kutta method with four stages, for additively partitioned systems of ordinary differential equations. Our main objective is that it will be useful as a horizontally explicit and vertically implicit (HEVI) method for atmospheric models. In our method the diagonal coefficients in the implicit part are all equal, and the HEVI-stability properties seem to be excellent. Further, the accuracies obtained for two simple test problems, used with different resolutions and integration intervals, considerably surpass those of a third order one step Runge-Kutta method also with four stages, used for comparison.


Atmospheric model

Two step Runge-Kutta method

Partitioned method

Time integration


Göran Christer Starius

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Tellus, Series A: Dynamic Meteorology and Oceanography

0280-6495 (ISSN) 1600-0870 (eISSN)

Vol. 75 1 172-178


Rymd- och flygteknik


Datavetenskap (datalogi)



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