ROS3P
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.
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References in zbMATH (referenced in 45 articles , 1 standard article )
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