TY - JOUR
T1 - An enhanced fictitious time integration method for non-linear algebraic equations with multiple solutions
T2 - Boundary layer, boundary value and eigenvalue problems
AU - Liu, Chein Shan
AU - Yeih, Weichung
AU - Atluri, Satya N.
PY - 2010
Y1 - 2010
N2 - When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of a repellor in the theory of nonlinear dynamical systems, to situations where multiple-solutions exist. We label this enhanced method as MSFTIM. MSFTIM is applied and illustrated in this paper through solving boundary-layer problems, boundary-value problems, and eigenvalue problems with multiple solutions.
AB - When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of a repellor in the theory of nonlinear dynamical systems, to situations where multiple-solutions exist. We label this enhanced method as MSFTIM. MSFTIM is applied and illustrated in this paper through solving boundary-layer problems, boundary-value problems, and eigenvalue problems with multiple solutions.
KW - Attracting set
KW - Multiple- Solution Fictitious Time Integration Method (MSFTIM)
KW - Non-linear algebraic equations
KW - Ordinary differential equations
KW - Repellor
UR - http://www.scopus.com/inward/record.url?scp=77954617718&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:77954617718
SN - 1526-1492
VL - 59
SP - 301
EP - 323
JO - CMES - Computer Modeling in Engineering and Sciences
JF - CMES - Computer Modeling in Engineering and Sciences
IS - 3
ER -