ISSN:
1069-8299
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A procedure was implemented to determine the optimum values for the two parameters of the Zienkiewicz three-level time schemes which could be utilized for the numerical solution of a system of ordinary differential equations. A multivariable search method was implemented to estimate optimum values for these parameters. The resultant optimum three-level time scheme produced very accurate results, satisfied physical reality, and did not produce any oscillations for the various problems that were investigated. The optimum values for the two parameters β and γ in the three-level scheme were β = 0·50005 and γ = 1·0007. A comparison was made between this optimum scheme and other existing three-level time schemes. The optimum scheme demonstrated superior results for all the problems that were analysed. However, the results of the optimization analysis produced a set of optimum parameters that were identical to the values that would reduce the general three-level time scheme into a central-difference two-level time scheme, i.e. β = 1/2 and γ = 1.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cnm.1640091203
