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Title: Forward–backward-difference time-integrating schemes with higher order derivatives for non-linear finite element analysis of solids and structures
Authors: Kaunda, MAE 
Keywords: Nonlinear dynamics;Implicit time-integrating schemes;Higher-order derivatives;One-step multiple-value methods;Spectral radius;Liapunov stability
Issue Date: 2015
Publisher: Elsevier
Abstract: One-step multiple-value methods are developed which involve an accurate predictor method with higher derivatives, followed by a corrector method cast in form of an enhanced Newton–Raphson scheme. The generalized Newmark (GNpj) method may be recovered as a special case. The algorithms serve to match the accuracy of the fourth-order Runge–Kutta–Fehlberg method. Challenges to solve more reliably, accurately and efficiently non-linear differential equations are highlighted as stemming from amplitude and phase shift errors introduced by discretization in space and time – a continuous-discrete transformation. The classical stability tool of spectral radius is performed on linear systems whereas Liapunov method on nonlinear systems.
Appears in Collections:Eng - Journal articles (DHET subsidised)

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