Quadrature methods for stiff ordinary differential systems

Abstract

The quadrature methods are based upon a substitution of an explicit A-stable first approximation into a generalized convolution formula. They are A-stable, explicit, and of arbitrarily high order. The generalized convolution formula is derived and its order-raising properties examined. Two families of explicit A-stable first approximations are developed, generalizing results of Lawson and Nørsett. Various aspects of the numerical implementation are discussed. Numerical results supplement the paper and exemplify the various merits and weaknesses of the quadrature methods.