OPTIMAL UNIFORM FINITE DIFFERENCE SCHEMES OF ORDER TWO FOR STIFF INITIAL VALUE PROBLEMS.

The paper presents finite difference schemes of order two for stiff initial-value problems, with a small parameter ∊ multiplying the first derivative. The schemes are a modified form of the classical trapezoidal rule. They are both optimal and uniform with respect to the small parameter ∊, that is, the solution of the difference schemes satisfies error estimates of the form | u(ti)-ui| ⩽ C min(h²,∊) where C is independent of i, h and ∊. Here h is the mesh size and ti is any mesh point. The schemes presented in this paper are different from the scheme of order two available in the literature. Finally, numerical experiments are presented. [ABSTRACT FROM AUTHOR]