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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References
Frank, R., Ueberhuber, C.W.: Iterated Defect Correction for the Efficient Solution of Stiff Systems of Ordinary Differential Equations. BIT17, 146–159 (1977)
Frank, R., Hertling, J., Lehner, H.:B-convergence Properties of Defect Correction Methods. Part II. Report Nr. 58/84, Institute for Applied and Numerical Mathematics, Technical University of Vienna, 1984
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Frank, R., Hertling, J. & Lehner, H. B-convergence properties of defect correction methods. II. Numer. Math. 49, 163–188 (1986). https://doi.org/10.1007/BF01389622
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DOI: https://doi.org/10.1007/BF01389622