Numerical Path Following and Eigenvalue Criteria for Branch Switching

Methods for numerical path following for nonlinear eigenvalue problems are studied. Euler Newton continuation along curves parameterized by a semi arclength is described. Criteria for localizing singular points (turning points or bifurcations) by means of a linear eigenproblem are introduced. It is found that a nonlinear version of the spectral transformation used for linear symmetric eigenproblems gives a surprisingly accurate prediction of the position of a singular point and the direction of bifurcating branches. Practical applications are discussed and numerical examples are reported.