A modification of the method of continuous prolongation for finding the bifurcation solutions of steady-state self-adjoint boundary value problems

Abstract

An algorithm for showing solution of systems of non-linear algebraic equations describing the steady-state behaviour of objects in the mechanics of a deformable solid is considered. The existence of limit points and simple bifurcation points on the trajectory of the solution of the system is admitted and, at these points, the Jacobian matrix of the system, assumed to be real, symmetric and continuous, degenerates. The basis of the algorithm is a transformation of the space of the arguments of the solution of systems of non-linear algebraic equations using a rotation matrix formed from the eigenvectors of the Jacobian matrix.