Algorithm to construct bifurcation structure of non-linear boundary problem for von Karman equations
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2017.1.0.08Keywords:
von Karman equations, solution branching of non-linear boundary problems for partial differential equations, primary and secondary bifurcation pathsAbstract
In the frameworks of the generalized Kantorovich method, a novel approach to detect and analyze singular points of a non-linear boundary problem for von Karman equations is proposed: an algorithm suggests that a sequence of single-dimensional boundary problems is constructed in order to solve the two-dimensional boundary problem in question. The aforesaid single-dimensional boundary problems are reduced to the equivalent Cauchy problems. In doing so, one calculates the Frechet matrix, whose degeneracy is necessary and sufficient conditions of branching. The simulation reveals the bifurcation structure for von Karman equations with the constant right term. In that case, the structure includes primary and secondary bifurcation paths.References
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