A scheme for tracing the equilibrium path in perturbation methods Original Research Article

A limitation on the use of perturbation methods for determining the equilibrium paths in nonlinear problems is the small size of the domain of convergence of the asymptotic expansion. In this paper a scheme for enlarging the radius of convergence of the expansion is presented. The scheme is based on a minimization process of the residual norm with respect to the forcing parameter together with a new polynomial interpolation of that same parameter. This has a regularizing effect also for equilibrium points far from the initial point where the solution is known. Some tests were carried out to evaluate the performance of the method.