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A mountain pass method for the numerical solution of semilinear wave equations

Choi, Y.S.; McKenna, P.J.; Romano, Marc (1993), A mountain pass method for the numerical solution of semilinear wave equations, Numerische Mathematik, 64, 1, p. 487-509. http://dx.doi.org/10.1007/BF01388701

Type
Article accepté pour publication ou publié
Date
1993
Journal name
Numerische Mathematik
Volume
64
Number
1
Publisher
Springer
Pages
487-509
Publication identifier
Metadata
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Author(s)
Choi, Y.S.
McKenna, P.J.
Romano, Marc
Abstract (EN)
It is well-known that periodic solutions of semilinear wave equations can be obtained as critical points of related functionals. In the situation that we studied, there is usually an obvious solution obtained as a solution of linear problem. We formulate a dual variational problem in such a way that the obvious solution is a local minimum. We then find additional non-obvious solutions via a numerical mountain pass algorithm, based on the theorems of Ambrosetti, Rabinowitz and Ekeland. Numerical results are presented.
Subjects / Keywords
linear problem; numerical mountain pass algorithm; semilinear wave equations