A new steplength control for continuation with the asymptotic numerical method

The continuation method, based on the asymptotic numerical method, to compute solution branches of nonlinear problems depending upon a parameter, has been applied with success to a wide variety of problems in fluids and elasticity. Two methods for the steplength selection have been previously used. In this paper we propose a new strategy for the steplength choice which is more mathematically sound and yields a better control of the local truncation error.