Numerical Approximation of Transcritical Simple Bifurcation Point of the Navier-Stokes Equations

Abstract

The extended system of nondegenerate simple bifurcation point of the Navier-Stokes equations is constructed in this paper. Due to its derivative has a block lower triangular form, we design a Newton-like method. Using the extended system and splitting iterative technique to compute transcritical nondegenerate simple bifurcation point, we not only reduce computational complexity, but also obtain quadratic convergence of algorithm.