SomeL-stable methods for stiff differential equations

A recent paper by Steihaug and Wolfbrandt [6] gives a second-order method for stiff differential equations, which includes an error estimate. We show how, in most practical circumstances, the error estimate can be obtained more simply, and derive two third-order methods along similar lines. All the methods described are single-step and linearly implicit, and they are designed to avoid frequent evaluations of the Jacobian and inversion of the associated matrix.