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Russian Academy of Sciences
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IssuesArchive of Issues2012-6pp.715-721

Archive of Issues

Total articles in the database: 1774
In Russian (): 975
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 76, Issue 6 / 2012 | Next article >>
Ye.A. Lopanitsyn and A.B. Frolov, "A modification of the method of continuous prolongation for finding the bifurcation solutions of steady-state self-adjoint boundary value problems," J. Appl. Math. Mech. 76 (6), 715-721 (2012)
Year 2012 Volume 76 Issue 6 Pages 715-721
Title A modification of the method of continuous prolongation for finding the bifurcation solutions of steady-state self-adjoint boundary value problems
Author(s) Ye.A. Lopanitsyn (Moscow, Russia, eal@mami.ru)
A.B. Frolov (Moscow, Russia)
Abstract An algorithm for showing solution of systems of non-linear algebraic equations describing the steady-state behaviour of objects in the mechanics of a deformable solid is considered. The existence of limit points and simple bifurcation points on the trajectory of the solution of the system is admitted and, at these points, the Jacobian matrix of the system, assumed to be real, symmetric and continuous, degenerates. The basis of the algorithm is a transformation of the space of the arguments of the solution of systems of non-linear algebraic equations using a rotation matrix formed from the eigenvectors of the Jacobian matrix.
Received 12 April 2012
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892813000300
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