An efficient algorithm for the determination of certain bifurcation points

AbstractMany practical problems require information about a branch of solutions of a system of nonlinear equations dependent upon a scalar parameter. We discuss some techniques for following such a branch through a turning point and describe an efficient method, with second order convergence, for finding the turning point. We also show that, if extra information is available about the solution branch, the method can be successfully applied to finding simple bifurcation points