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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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##### References:
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