High-order predictor-corrector algorithms

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 Pade 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 (C) 2002 John Wiley Sons, Ltd.