An Enhanced Fictitious Time Integration Method for Non-Linear Algebraic Equations With Multiple Solutions: Boundary Layer, Boundary Value and Eigenvalue Problems
Resource
Computer Modeling in Engineering & Sciences, 59(3), 301-324
Journal
Computer Modeling in Engineering & Sciences
Journal Volume
59
Journal Issue
3
Pages
301-324
Date Issued
2010
Date
2010
Author(s)
Liu, Chein-Shan
Yeih, Weichung
Atluri, Satya N.
Abstract
equations appear naturally. In a recent paper by Liu and Atluri, non-linear alge-braic 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 il-lustrated in this paper through solving boundary-layer problems, boundary-value problems, and eigenvalue problems with multiple solutions.
Type
journal article
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