Fourth Order Partitioned Methods Designed for the Time Integration of Atmospheric Models

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 horizontally explicit and vertically implicit (HEVI) atmospheric models. our the diagonal coefficients in part are all equal, HEVI-stability properties seem to excellent. Further, accuracies obtained simple test problems, used different resolutions integration intervals, considerably surpass those third one also comparison.