An Enhanced Fictitious Time Integration Method for Non-Linear Algebraic Equations With Multiple Solutions: Boundary Layer, Boundary Value and Eigenvalue Problems

作者：Liu Chein Shan^*; Yeih Weichung; Atluri Satya N

来源：Computer Modeling in Engineering & Sciences, 2010, 59(3): 301-323.

• Non-linear algebraic equations
• Ordinary differential equations
• Multiple-Solution Fictitious Time Integration Method (MSFTIM)
• Repellor
• Attracting set

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.

• 出版日期2010-4