A Bisection-Like Algorithm for Branch Switching at a Simple Branch Point

摘要

At a Simple Branch Point x_0 of a parameter-dependent nonlinear system, two distinct solutions branches S_1 and S_2 intersect. A popular method of branch switching from S_1 to S_2 at x_0 is to use an orthogonal vector to the tangent vector to S_1 at x_0 as an initial guess for the tangent vector to S_2 at x_0. We describe an improved version of this method using a bisection-like procedure, which is especially useful for large problems.