A Contribution to One-step Multiple-Value Methods for Computational Analysis of Problems in Non-Linear Dynamics

摘要

One-step multiple-value methods are developed for solving problems in nonlinear dynamics which involve an accurate predictor method with higher derivatives, followed by a corrector method cast in form of an enhanced Newton-Raphson scheme. An algorithm, supported by numerical examples, is developed to determine initial conditions of the higher derivatives necessary for the one-step multiple-value methods. Further, a Laplace transform method is also proposed to determine initial conditions. The generalized Newmark (GNpj) method of Zienkiewicz and Taylor may be recovered as a special case. The classical stability tool of spectral radius is performed on linear systems whereas Liapunov method on nonlinear systems.