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A continuation method based on a high order predictor and an adaptive steplength control
Author(s) -
Gervais J.J.,
Sadiky H.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310125
Subject(s) - continuation , taylor series , nonlinear system , path (computing) , polynomial , mathematics , mathematical optimization , order (exchange) , selection (genetic algorithm) , computer science , algorithm , mathematical analysis , artificial intelligence , physics , finance , quantum mechanics , economics , programming language
To compute solution paths of nonlinear systems F ( x ,λ) ≡ 0 depending upon a real parameter we propose a predictor‐corrector continuation method based on the third order Taylor polynomial or the (2,1)‐Padé approximation as predictor. The Taylor coefficients are computed using the exact expressions of the second and third orders derivatives of F . Our method works with any of the parametrizations: Pseudo‐arclength, local or secant length. A strategy for an adaptive steplength selection well suited for this high order predictor is derived which allows a good control of the accuracy with which the solution path is traced. Numerical examples demonstrate the efficiency of our method and give comparisons with previously proposed methods.