E. A. Novikov, “Maximal order of accuracy of <nobr>$(m, 1)$</nobr>-methods for solving stiff problems”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 3(24),Pages <nobr>100

This article is cited in 1 paper

Mathematical Modeling

Maximal order of accuracy of $(m, 1)$-methods for solving stiff problems

E. A. Novikov^ab

^a Dept. of Computational Mathematics, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
^b Dept. of Mathematical Software for Systems and Discrete Devices, Siberian Federal University, Krasnoyarsk

Abstract: We investigate $(m, 1)$-methods for solving stiff problems in which the right part of system of the differential equations is calculated one times on each step. It is shown that the maximal order of accuracy of the $L$-stability $(m, 1)$-method is equal to two, and the method of the maximal order is constructed.

Keywords: stiff problems, Rosenbrock schemes, $(m, k)$-methods, $A$-stability, $L$-stability.

UDC: 519.622

MSC: Primary 65L20; Secondary 65L05, 34A34

Original article submitted 28/I/2011
revision submitted – 17/VIII/2011

DOI: 10.14498/vsgtu920