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M.A.E. Kaunda, "A Contribution to One-step Multiple-Value Methods for Computational Analysis of Problems in Non-Linear Dynamics", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 109, 2015. doi:10.4203/ccp.108.109

Keywords: nonlinear dynamics, implicit time-integrating schemes, higher-order derivatives, one-step multiple-value methods, spectral radius, Liapunov stability.

Summary

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.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 108 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping Paper 109 A Contribution to One-step Multiple-Value Methods for Computational Analysis of Problems in Non-Linear Dynamics M.A.E. Kaunda Cape Peninsula University of Technology, Bellville, South Africa doi:10.4203/ccp.108.109 purchase the full-text of this paper Full Bibliographic Reference for this paper M.A.E. Kaunda, "A Contribution to One-step Multiple-Value Methods for Computational Analysis of Problems in Non-Linear Dynamics", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 109, 2015. doi:10.4203/ccp.108.109 Keywords: nonlinear dynamics, implicit time-integrating schemes, higher-order derivatives, one-step multiple-value methods, spectral radius, Liapunov stability. Summary 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. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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