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.
|Number of pages||23|
|Journal||CMES - Computer Modeling in Engineering and Sciences|
|State||Published - 2010|
- Attracting set
- Multiple- Solution Fictitious Time Integration Method (MSFTIM)
- Non-linear algebraic equations
- Ordinary differential equations