High-order predictor-corrector algorithms

New predictor–corrector algorithms are presented for the computation of solution paths of non-linear partial di erential equations. The predictors and the correctors are based on perturbation techniques and Pad e approximants. This extends the Asymptotic Numerical Method (ANM), which is an e cient highorder continuation technique without corrector. The e ciency 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