An iterative process based on homotopy and perturbation techniques Original Research Article

In this paper, we discuss high order iterative methods whose principle has been presented recently (N. Damil, M. Potier-Ferry, A. Najah, R. Chari, R. Lahmam, Communications in Numerical Methods in Engineering 15 (1999) 701–708). These algorithms are optimised by appropriate choices of the homotopy transformation, of the perturbation technique and of the strategy of control. Especially, the use of Padé approximants yields very efficient algorithms as compared with classical first order ones. A classical non-linear elastic shell problem permits us to assess the efficiency of the proposed method.