ROS3P swMATH ID: 813 Software Authors: Lang, J.; Verwer, J. Description: ROS3P – An accurate third-order Rosenbrock solver designed for parabolic problems WWe present a new Rosenbrock solver which is third-order accurate for nonlinear parabolic problems. Since Rosenbrock methods suffer from order reduction when they are applied to partial differential equations, additional order conditions have to be satisfied. Although these conditions have been known for a longer time, from the practical point of view only little has been done to construct new methods. G. Steinebach [Order-reduction of ROW-methods for DAEs and method of lines applications, Preprint 1741, Technische Hochschule Darmstadt, Germany (1995)] modified the well-known solver RODAS of E. Hairer and G. Wanner [Solving ordinary differential equations. II: Stiff and differential-algebraic problems. 2nd rev. ed. (1996; Zbl 0859.65067)] to preserve its classical order four for special problem classes including linear parabolic equations. His solver RODASP, however, drops down to order three for nonlinear parabolic problems. Our motivation here was to derive an efficient third-order Rosenbrock solver for the nonlinear situation. Such a method exists with three stages and two function evaluations only. A comparison with other third-order methods shows the substantial potential of our new method. Homepage: http://oai.cwi.nl/oai/asset/1102/1102A.pdf Keywords: comparison of methods; method of lines; nonlinear parabolic equations; Rosenbrock methods; order reduction; third-order methods Related Software: RODAS; PETSc; MooNMD; KARDOS; Spalart-Allmaras; UMFPACK; ROWMAP; RODASP; FEATFLOW; METIS; dsoa; MEBDF; DifferentialEquations.jl; KELLEY; DUNE; PARDISO; Robust Control Toolbox; Pascal-SC; OPTRAGEN; VPLAN Cited in: 47 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year ROS3P – An accurate third-order Rosenbrock solver designed for parabolic problems. Zbl 0996.65099Lang, J.; Verwer, J. 2001 all top 5 Cited by 93 Authors 8 Rang, Joachim 7 Lang, Jens 6 Bassi, Francesco 5 Crivellini, Andrea 4 Colombo, Alessandro G. 4 Ghidoni, Antonio 4 Massa, Francesco Carlo 3 Weiner, Rüdiger 2 Angermann, Lutz 2 Bänsch, Eberhard 2 Botti, Lorenzo 2 Clever, Debora 2 Falcke, Martin 2 Hartmann, Stefan 2 John, Volker 2 Nagaiah, Chamakuri 2 Nigro, Alessandra 2 Podhaisky, Helmut 2 Rebay, Stefano 2 Rüdiger, Sten 2 Sandu, Adrian 2 Tamma, Kumar K. 2 Warnecke, Gerald G. 2 Weller, Stephan 1 Becker, Urs 1 Bott, Stefanie 1 Braatz, Richard D. 1 Burger, Michaek 1 Clemens, Markus 1 Colli Franzone, Piero 1 D’Alessandro, Valerio 1 Davidson, Jane H. 1 Debrabant, Kristian 1 Deuflhard, Peter 1 Di Pietro, Daniele Antonio 1 Diblík, Josef 1 Domoshnitsky, Alexander I. 1 Erdmann, Bodo 1 Fabien, Brian C. 1 Franchina, Nicoletta 1 Franciolini, Matteo 1 Garrick, Sean C. 1 Gerisch, Alf 1 Glandon, S. Ross 1 Goldstein, R. J. 1 González-Pinto, Severiano 1 Günther, Michael 1 Hamkar, Ahmad-Wahadj 1 Heberlein, J. V. R. 1 Hernandez-Abreu, Domingo 1 Ibele, W. E. 1 Jebens, Stefan 1 Karasözen, Bülent 1 Kishida, Masako 1 Knoth, Oswald 1 Kortshagen, U. 1 Kuehn, T. H. 1 Kulacki, Francis A. 1 Li, Tongxing 1 Liao, Wenyuan 1 Mahnken, Rolf 1 Matthies, Gunar 1 Maxam, Dean 1 Novati, Paolo 1 Noventa, G. M. 1 Patankar, Suhas V. 1 Pavarino, Luca Franco 1 Pérez Rodríguez, S. 1 Qin, Guoliang 1 Roberts, Steven P. 1 Rogovchenko, Yuriy V. 1 Sadyrbaev, Felix Zh. 1 Sarıaydın-Filibelioğlu, Ayşe 1 Sarshar, Arash 1 Schmitt, Bernhard A. 1 Schröder, Dirk 1 Simeon, Bernd 1 Simon, T. W. 1 Steinebach, Gerd 1 Strykowski, Paul J. 1 Teleaga, Delia 1 Tranquilli, Paul 1 Ulbrich, Stefan 1 Uzunca, Murat 1 Verwer, Jan G. 1 Wang, Lai 1 Wang, Qiru 1 Wang, Yazhou 1 Wensch, Jörg 1 Wimmer, Georg 1 Xue, Tao 1 Yu, Meilin 1 Ziems, Jan Carsten all top 5 Cited in 15 Serials 7 Computers and Fluids 6 Computer Methods in Applied Mechanics and Engineering 6 Journal of Computational and Applied Mathematics 6 Applied Numerical Mathematics 3 BIT 3 Optimal Control Applications & Methods 2 Abstract and Applied Analysis 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Applied Mathematics and Computation 1 Computational Mechanics 1 Journal of Scientific Computing 1 SIAM Journal on Scientific Computing 1 European Journal of Mechanics. B. Fluids 1 Advances in Differential Equations and Control Processes all top 5 Cited in 13 Fields 36 Numerical analysis (65-XX) 16 Fluid mechanics (76-XX) 11 Partial differential equations (35-XX) 8 Ordinary differential equations (34-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) Citations by Year