TITLE:
A New Class of Vector Padé Approximants in the Asymptotic Numerical Method: Application in Nonlinear 2D Elasticity
AUTHORS:
Abdellah Hamdaoui, Rachida Hihi, Bouazza Braikat, Noureddine Tounsi, Noureddine Damil
KEYWORDS:
Vector Padé Approximants; Asymptotic Numerical Method; Nonlinear Elasticity
JOURNAL NAME:
World Journal of Mechanics,
Vol.4 No.2,
February
18,
2014
ABSTRACT: The Asymptotic Numerical Method (ANM) is a family of
algorithms for path following problems, where each step is based on the
computation of truncated vector series [1]. The Vector Padé approximants were
introduced in the ANM to improve the domain of validity of vector series and to
reduce the number of steps needed to obtain the entire solution path [1,2]. In
this paper and in the framework of the ANM, we define and build a new type of
Vector Padé approximant from a truncated vector series by extending the
definition of the Padé approximant of a scalar series without any
orthonormalization procedure. By this way, we define a new class of Vector Padé
approximants which can be used to extend the domain of validity in the ANM
algorithms. There is a connection between this type of Vector Padé approximant
and Vector Padé type approximant introduced in [3, 4]. We show also that the
Vector Padé approximants introduced in the previous works [1,2], are special
cases of this class. Applications in 2D nonlinear elasticity are presented.