OPTIMAL UNIFORM FINITE-DIFFERENCE SCHEMES OF ORDER 2 FOR STIFF INITIAL-VALUE PROBLEMS

The paper presents finite difference schemes of order two for stiff in itial-value problems, with a small parameter epsilon multiplying the f irst derivative. The schemes are a modified form of the classical trap ezoidal rule. They are both optimal and uniform with respect to the sm all parameter epsilon, that is, the solution of the difference schemes satisfies error estimates of the form \u(t(i)) - u(i)\ less-than-or-e qual-to C min (h2, epsilon) where C is independent of i, h and epsilon . Here h is the mesh size and t(i) is any mesh point. The schemes pres ented in this paper are different from the scheme of order two availab le in the literature. Finally, numerical experiments are presented.