The Deferred Correction Procedure for Linear Multistep Formulas

Abstract

A general approach of deferred correction procedure based on linear multistep formulas is proposed. Several deferred correction procedures based on backward differentiation formulas, which allow us to develop L-stable algorithms of order up to 4 and $L(\alpha)$-stable algorithms of order up to 7, are derived. Preliminary numerical results indicate that this approach is indeed efficient.