An enhanced fictitious time integration method for non-linear algebraic equations with multiple solutions: Boundary layer, boundary value and eigenvalue problems

Chein Shan Liu; Weichung Yeih; Satya N. Atluri

An enhanced fictitious time integration method for non-linear algebraic equations with multiple solutions: Boundary layer, boundary value and eigenvalue problems

Chein Shan Liu, Weichung Yeih, Satya N. Atluri

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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 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.

Original language	English
Pages (from-to)	301-323
Number of pages	23
Journal	CMES - Computer Modeling in Engineering and Sciences
Volume	59
Issue number	3
State	Published - 2010

Keywords

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

Cite this

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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 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.",

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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. / Liu, Chein Shan; Yeih, Weichung; Atluri, Satya N.
In: CMES - Computer Modeling in Engineering and Sciences, Vol. 59, No. 3, 2010, p. 301-323.

Research output: Contribution to journal › Article › peer-review

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AU - Yeih, Weichung

AU - Atluri, Satya N.

PY - 2010

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KW - Multiple- Solution Fictitious Time Integration Method (MSFTIM)

KW - Non-linear algebraic equations

KW - Ordinary differential equations

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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

Abstract

Keywords

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