An explicit two-step method exact for the scalar test equation y′ = λy

An explicit two-step method exact for the scalar test equation y′ = λy, Re(λ) < 0 is presented in this paper. It is exponentially fitted, L-stable (thus, A-stable), and of order 2. With a new set of vector computations, we also extend directly the method to systems of ordinary differential equations. The numerical experiments demonstrate that this explicit two-step method is suitable for stiff systems.