SUFFICIENT CONDITIONS FOR UNIFORMLY 2ND-ORDER CONVERGENT SCHEMES FOR STIFF INITIAL-VALUE PROBLEMS

We present a convergence analysis for a class of one-step, exponentially fitted, finite difference schemes for stiff initial-value problems. Such schemes, when applied to the numerical integration of the linear scalar problem epsilony' + a(x)y = f(x), x is-an-element-of (0, X), with y(0) given and where epsilon > 0 is a small parameter, give solutions satisfying a uniform (in epsilon) error estimate. In this paper, a set of sufficient conditions for uniform second-order convergence is derived. The findings differ from those reported in [1-3], and are complemented by the results of numerical experiments which illustrate the effectiveness of the proposed approach.