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 convergence of these methods derived under the assumption that.hL is 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 Hypothesis A 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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Frank, R., Hertling, J. & Lehner, H. B-convergence properties of defect correction methods. I. Numer. Math. 49, 139–162 (1986). https://doi.org/10.1007/BF01389621
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DOI: https://doi.org/10.1007/BF01389621