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Order barriers for the B-convergence of ROW methods. (English) Zbl 0662.65070
This paper investigates the error of Rosenbrock methods when they are applied to the Prothero-Robinson problem \(y'=\lambda (y-g(x))+g'(x).\) The method is called \(B_{PR}\)-convergent of order q, if the global error is bounded by \(C\cdot h^ q\) uniformly for h, \(\lambda\) with \(Re h\lambda <\Lambda_ 0<0\) and \(h\leq \overline{h}\). The main result is that for m- stage Rosenbrock methods of classical order \(p=m+1\), \(p=m\), and \(p=m-1\), the order of \(B_{PR}\)-convergence cannot exceed 2, 3, and 5, respectively. Methods with maximal order of \(B_{PR}\)-convergence are constructed.
Reviewer: E.Hairer

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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