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1. Global asymptotic stability of certain third-order nonlinear differential equations.

Author

Zhang, Lijuan and Yu, Lixin

Subjects
*STABILITY theory, *NUMERICAL solutions to nonlinear differential equations, *MATHEMATICAL analysis, *LYAPUNOV functions, *NUMERICAL analysis, *DIFFERENTIAL equations
Abstract

In this paper, we give some sufficient conditions to guarantee global asymptotic stability of the zero solution of the third-order nonlinear differential equation: x ′ ′ ′ + g( x, x ′ , x ′ ′ ) + f( x, x ′ ) x ′ + h( x) = 0. Two examples are also given to illustrate our results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2013
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2. Stability analysis of one-leg methods for nonlinear functional differential and functional equations

Author

Yu, Yuexin and Wen, Liping

Subjects
*NUMERICAL solutions to functional equations, *NUMERICAL solutions to nonlinear differential equations, *STABILITY (Mechanics), *ASYMPTOTIC expansions, *GLOBAL analysis (Mathematics), *NUMERICAL analysis, *MATHEMATICAL analysis
Abstract

Abstract: This paper is concerned with the numerical solution of nonlinear functional differential and functional equations. The adaptation of one-leg methods is considered. It is proved that an A-stable one-leg method is globally stable and a strongly A-stable one-leg method is asymptotically stable under suitable conditions. A numerical test is given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Published
2010
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