# zbMATH — the first resource for mathematics

Rosenbrock-type ‘peer’ two-step methods. (English) Zbl 1072.65107
The authors construct $$s$$-stage methods for solving initial value problems for stiff ordinary differential equations where all stage values have stage order $$s-1.$$ The proposed class of methods is stable in the sense of zero-stability for arbitrary stepsize sequences. Using the concept of effective order the authors derive methods having order $$s$$ for constant stepsizes.

##### MSC:
 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65Y05 Parallel numerical computation 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
ROS3P
Full Text:
##### References:
 [1] Butcher, J.; Wright, W., The construction of general linear methods, Bit, 43, 695-721, (2003) · Zbl 1046.65054 [2] Butcher, J.C., Order and effective order, Appl. numer. math., 28, 179-191, (1998) · Zbl 0927.65095 [3] Butcher, J.C., Numerical methods for ordinary differential equations, (2003), Wiley New York · Zbl 1032.65512 [4] Hairer, E.; Wanner, G., Solving ordinary differential equations II, (1996), Springer Berlin · Zbl 0859.65067 [5] Jackiewicz, Z.; Podhaisky, H.; Weiner, R., Construction of highly stable two-step W-methods for ordinary differential equations, J. comput. appl. math., 167, 389-403, (2004) · Zbl 1049.65070 [6] Kreiss, H.O., Difference methods for stiff ordinary differential equations, SIAM J. numer. anal., 15, 21-58, (1978) · Zbl 0385.65035 [7] Lang, J.; Verwer, J.G., ROS3P—an accurate third-order rosenbrock solver designed for parabolic problems, Bit, 41, 731-738, (2001) · Zbl 0996.65099 [8] Podhaisky, H.; Schmitt, B.A.; Weiner, R., Design, analysis and testing of some parallel two-step W-methods for stiff systems, Appl. numer. math., 42, 381-395, (2002) · Zbl 1005.65073 [9] H. Podhaisky, B.A. Schmitt, R. Weiner, Linearly-implicit two-step methods and their implementation in Nordsieck-form, submitted for fublication · Zbl 1089.65068 [10] Schmitt, B.A.; Weiner, R., Parallel two-step W-methods with peer variables, SIAM J. numer. anal., 42, 265-282, (2004) · Zbl 1089.65070 [11] B.A. Schmitt, R. Weiner, K. Erdmann, Implicit Parallel Peer Methods for stiff initial value problems, Report 2003-7, Reihe Mathematik, Universität Marburg · Zbl 1072.65108 [12] B.A. Schmitt, R. Weiner, H. Podhaisky, Multi-implicit peer two-step W-methods for parallel time integration, submitted for fublication · Zbl 1079.65082 [13] Steinebach, G.; Rentrop, P., An adaptive method of lines approach for modelling flow and transport in rivers, (), 181-205 [14] Weiner, R.; Schmitt, B.A.; Podhaisky, H., Two-step W-methods and their application to MOL-systems, Appl. numer. math., 48, 425-439, (2004) · Zbl 1042.65072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.