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The solution of higher order integration formulae for dynamic response equations by the conjugate gradient method
Author(s) -
Carter A. L.,
Shiflett G. R.,
Laub A. J.
Publication year - 1984
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.1620200212
Subject(s) - conjugate gradient method , mathematics , conjugate , degrees of freedom (physics and chemistry) , order (exchange) , dynamic equation , mathematical analysis , mathematical optimization , physics , nonlinear system , finance , quantum mechanics , economics
Higher order implicit integration techniques for solving dynamic response equations are derived utilizing Padé approximations. In an effort to minimize the disadvantages of using these higher order formulae to obtain solutions to systems with large numbers of degrees‐of‐freedom, the conjugate gradient method is employed to solve for the displacements. The accuracy and efficiency of the techniques are evaluated by making comparisons between known analytical and calculated results.