B-convergence properties of defect correction methods. II

Abstract

Summary. B-convergence properties of defect correction methods based on the implicit Euler and midpoint schemes are discussed. The property of Bconvergence means that there exist global error bounds for nonlinear stiff problems independent of their stiffness. It turns out that the orders of Bconvergence of these methods coincide with the conventional orders of convergence of these methods derived under the assumption that h L is small (where L 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.