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Analysis of static non‐linear response by explicit time integration
Author(s) -
Oden J. T.,
Key J. E.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620070211
Subject(s) - algebraic number , algebraic equation , mathematics , linear system , system of linear equations , linear dynamical system , relaxation (psychology) , lti system theory , basis (linear algebra) , dynamical systems theory , construct (python library) , differential equation , linear differential equation , linear equation , invariant (physics) , computer science , mathematical analysis , nonlinear system , geometry , physics , psychology , social psychology , quantum mechanics , mathematical physics , programming language
In general, a system of linear (or non‐linear) algebraic equations is solved on an analogue computer by integrating an appropriately defined system of associated first‐order differential equations, the steady‐state solution of which is the desired solution of algebraic system. This approach usually works very well so long as the associated dynamical system is stable. The idea of using the same approach numerically is also not altogether new. One can, ‘analogously’, construct a dynamical system associated with a given system of non‐linear algebraic equations and solve it numerically by any of a number of explicit time integration schemes. In fact, similar ideas provide the basis for certain ‘dynamic relaxation’ methods, incremental loading methods and the widely acclaimed methods of invariant imbedding.