Finding special points using matrix-free predictor-corrector methods

One of the main purposes of numerical continuation methods concerns the accurate determination of certain special points on the solution curve c(s) which is implicitly defined from a smooth map H:Rn+1→Rn. In this paper, matrix-free predictor-corrector methods in conjunction with adaptive steplength control is used to approximate the critical and fixed points of a smooth map. Some of numerical results are presented.