B-convergence properties of defect correction methods. II |
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Authors: | R Frank J Hertling H Lehner |
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Institution: | (1) Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstraß 6-8, A-1040 Wien, Österreich |
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Abstract: | Summary
B-convergence properties of defect correction methods based on the implicit Euler and midpoint schemes are discussed. The property ofB-convergence means that there exist global error bounds for nonlinear stiff problems independent of their stiffness. It turns out that the orders ofB-convergence of these methods coincide with the conventional orders of small (whereL is a Lipschitz constant of the right-hand side). In Part I these assertions are reduced to the validity of the so-called HypothesisA which is discussed in greater detail in Part II. Numerical experiments confirming the theoretical analysis are also given in Part II. |
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Keywords: | AMS(MOS): 65B99 65L05 CR: G 1 7 |
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