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
TypeArticle accepté pour publication ou publié
Journal nameNumerische Mathematik
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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 / Keywordslinear problem; numerical mountain pass algorithm; semilinear wave equations
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