| Titre : | Numeric-analytic form of the adomian decomposition method for two-point boundary value problems in nonlinear mechanics (2007) |
| Auteurs : | S. Ghosh, Auteur ; D. Roy, Auteur |
| Type de document : | Article : texte imprimé |
| Dans : | Journal of engineering mechanics (Vol. 133 N°10, Octobre 2007) |
| Article en page(s) : | pp. 1124-1133 |
| Note générale : | Mécanique appliquée |
| Langues : | Anglais |
| Tags : | Decomposition Numerical analysis Algorithms Differential equations |
| Résumé : | A new numeric-analytic technique is developed for two-point nonlinear boundary-value problems (BVPs) of engineering interest. The analytic part of the method is based on a conventional Adomian decomposition method (ADM). However, given a discretization of the one-dimensional domain, the present algorithm applies the ADM, repetitively over successive intervals and exploits a shooting algorithm to solve the BVPs. Apart from a very high rate of convergence as the discretization is made finer, yet another significant advantage of the method is that it provides the solution in a piecewise functional form and one can finally arrive at a continuous form of the global solution. The procedure is used to study planar, large-deflection (Elastica) problem of a cantilever beam subjected to a transverse, concentrated load, at its free end. Moreover the elastoplastic behavior of a cantilever is also studied. Comparisons with exact solutions as well as with results via a few other competing algorithms demonstrate the remarkable accuracy of the proposed method. |
| ISSN : | 0733-9399 |
| En ligne : | http://cedb.asce.org/cgi/WWWdisplay.cgi?160819 |
