This article is cited in 19 papers

Two-stage complex Rosenbrock schemes for stiff systems

A. B. Alshin^a, E. A. Alshina^a, A. G. Limonov<sup>b

a</sup> Institute of Mathematical Modeling, Russian Academy of Sciences, pl. Miusskaya 4a, Moscow, 125047, Russia
^b Moscow State Institute of Electronic Engineering (Technical University), Zelenograd, Moscow, 124498, Russia

Abstract: New two-stage Rosenbrock schemes with complex coefficients are proposed for stiff systems of differential equations. The schemes are fourth-order accurate and satisfy enhanced stability requirements. A one-parameter family of $L1$-stable schemes with coefficients explicitly calculated by formulas involving only fractions and radicals is constructed. A single $L2$-stable scheme is found in this family. The coefficients of the fourth-order accurate $L4$-stable scheme previously obtained by P. D. Shirkov are refined. Several fourth-order schemes are constructed that are high-order accurate for linear problems and possess the limiting order of $L$-decay. The schemes proposed are proved to converge. A symbolic computation algorithm is developed that constructs order conditions for multistage Rosenbrock schemes with complex coefficients. This algorithm is used to design the schemes proposed and to obtain fifth-order accurate conditions.

Key words: two-stage complex Rosenbrock schemes, stiff systems of ordinary differential equations, $L_p$-stable schemes, $A$-stability.

UDC: 519.622.2

Received: 26.02.2008
Revised: 06.06.2008

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:2, 261–278

Bibliographic databases:

• 
• 
• 
•