High‐order predictor–corrector algorithms

Abstract

Abstract New predictor–corrector algorithms are presented for the computation of solution paths of non‐linear partial differential equations. The predictors and the correctors are based on perturbation techniques and Padé approximants. This extends the Asymptotic Numerical Method (ANM), which is an efficient high‐order continuation technique without corrector. The efficiency and the reliability of the new technique are assessed by several examples within thin shell theory and Navier–Stokes equations. Many variants have been tested to establish an optimal algorithm. Copyright © 2002 John Wiley & Sons, Ltd.