Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0877.35126
Humphreys, L.D.
Numerical mountain pass solutions of a suspension bridge equation. (English)
[J] Nonlinear Anal., Theory Methods Appl. 28, No.11, 1811-1826 (1997). ISSN 0362-546X

The author develops a new global numerical method to find the large amplitude oscillations of a nonlinear model for suspension bridges. The central idea of the method is to find the solutions in a straightforward global way, without requiring good initial guesses as to where solutions might be. The framework of the algorithm is based on a work by Choi and McKenna. The mountain pass algorithm is a constructive implementation of the mountain pass theorems of Ambrosetti, Rabinowitz, and Ekeland.\par The basic idea of the method is quite intuitive. On a finite-dimensional approximation subspace, take a piecewise linear path joining the local minimum and a point whose image is lower. After calculating the maximum of the functional along the path, the path is deformed by pushing the point at which the maximum is located in the direction of the steepest descent. One repeats this step, stopping only when the critical point is reached. The algorithm is extremely robust and global in nature and it was tested in the cases where the mathematical proof guarantees the existence of large amplitude periodic solutions and when the solutions can be reduced to solutions of ordinary differential equations. Some solutions are obtained where there are no proofs of existence.
[L.Vazquez (Madrid)]

MSC 2000:: *35Q72 Other PDE from mechanics
65N99 Numerical methods for BVP of PDE
35G20 General theory of nonlinear higher-order PDE
35A15 Variational methods (PDE)

Keywords: mountain pass method; dual variational problem; suspension bridge equation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]