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

Chein-Shan Liu1, Weichung Yeih2, Satya N. Atluri3
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail:liucs@ntu.edu.tw
Department of Harbor & River Engineering and Computation and Simulation Center, National Taiwan Ocean University, Keelung, Taiwan.
Center for Aerospace Research & Education, University of California, Irvine

Computer Modeling in Engineering & Sciences 2010, 59(3), 301-324. https://doi.org/10.3970/cmes.2010.059.301

Abstract

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 arepellorin the theory ofnonlinear 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.

Keywords

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

Cite This Article

Liu, C., Yeih, W., Atluri, S. N. (2010). An Enhanced Fictitious Time Integration Method for Non-Linear Algebraic Equations With Multiple Solutions: Boundary Layer, Boundary Value and Eigenvalue Problems. CMES-Computer Modeling in Engineering & Sciences, 59(3), 301–324.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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