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A method of solution for non‐linear simultaneous algebraic equations
Author(s) -
Walker A. C.
Publication year - 1969
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.1620010206
Subject(s) - finite element method , algebraic equation , system of linear equations , linear system , mathematics , linear equation , taylor series , algebraic number , simultaneous equations , newton's method , computer science , mathematical analysis , nonlinear system , differential equation , engineering , physics , structural engineering , quantum mechanics
The solution of the large numbers of non‐linear algebraic equations occurring in analyses of non‐linear structural systems using finite differences or finite elements is time consuming even for the fastest computers. This paper presents a method of solution based on a Taylor's expansion technique which is an aid in the solution of such systems of equations. Examples presented show that in the finite element analysis of moderately non‐linear structural systems the technique provides sufficiently accurate solutions. For more non‐linear systems the technique provides excellent starting values for the Newton‐Raphson method.