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Optimization analysis of the four‐level‐time schemes
Author(s) -
Shayya Walid H.,
Segerlind Larry J.,
Bralts Vincent F.
Publication year - 1991
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.1620310606
Subject(s) - weighting , mathematics , ordinary differential equation , mathematical optimization , variable (mathematics) , scheme (mathematics) , galerkin method , differential equation , finite element method , engineering , mathematical analysis , structural engineering , medicine , radiology
A procedure was implemented to determine some optimum values for the parameters of the four‐level‐time scheme which can be utilized for the numerical solution of a system of ordinary differential equations. A multi‐variable search method was employed to estimate these optimum parameters. Two different optimization studies were performed. The resultant optimum four‐level‐time schemes produced very accurate results, satisfied physical reality, and did not produce any oscillations for the specific problems that were studied. The optimum values for the three parameters α, β and γ in the four‐level‐time scheme were α = 16.72, β = 6.26 and γ = 2.46. The optimum value of θ for the Wilson‐θ method was θ = 1.42. The optimum schemes were compared to some existing four‐level‐time schemes. The outcome demonstrated that the optimum schemes were superior. The Houbolt method and the Galerkin weighting procedure were shown to have greater inaccuracies than the optimum schemes.