Computation of maximal turning points to nonlinear equations by nonsmooth optimization. (2nd January 2016) - Il'yasov, Yavdat; Ivanov, Aleksandr
Abstract : We develop a new approach to finding bifurcations of solutions of nonlinear equation systems, which is based on the detection of extreme values of a new type of variational functional associated with the considered problems. The variational functional is obtained constructively by the extended functional method which can be applied to a wide class of parametric problems including nonlinear partial differential equations. Sufficient and necessary conditions for the existence of a maximal turning point by the approach are proved. Based on these, an algorithm of the quasi-direction of steepest ascent is introduced. Simulation experiments are used to illustrate the behaviour of the method and to discuss its advantages and disadvantages in comparison with the alternatives.