C&SA | Contents

Volume 56 >>> № 1 JANUARY — FEBRUARY 2020

UDC 519.62

V.A. Prusov¹, A.Yu. Doroshenko²

¹ Ukrainian Hydrometeorological Institute of the State Emergency Service of Ukraine and of the National Academy of Sciences of Ukraine, Kyiv, Ukraine

² National Technical University of Ukraine “Igor Sikorsky Kyiv
Polytechnic Institute,” Kyiv, Ukraine

doroshenkoanatoliy2@gmail.com

TESTING A MULTI-STEP SINGLE-STAGE METHOD ON HARD TASKS

Abstract. A multistep one-stage method is considered, which allows one to integrate hard differential equations and systems of equations with high accuracy and low computational costs. The examples show that the proposed method is not inferior to the best available methods in solving hard problems. The calculation results allow us to determine the absolute stability regions for a multistep one-stage method where it is possible to change the integration step over a wide range while maintaining the computational stability of the method.

Keywords: hard equations and systems, multistep one-stage method, (4,2) method, CROS, four-stage explicit Runge–Kutta method.

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