B-convergence properties of defect correction methods. I

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.