A novel method for computation of higher order singular points in nonlinear problems with single parameter

摘要

This paper deals with unusual numerical techniques for computation of higher order singular points in nonlinear problems with single parameter. Based on the uniformly extended system, a unified algorithm combining the homotopy and the pseudo-arclength continuation method is given. Properties of the uniformly augmented system are listed and proved. The effectiveness of the proposed algorithm is testified by three numerical examples.