OPTIMIZATION ANALYSIS OF THE 3-LEVEL TIME SCHEMES

A procedure was implemented to determine the optimum values for the tw o parameters of the Zienkiewicz three-level time schemes which could b e utilized for the numerical solution of a system of ordinary differen tial equations. A multivariable search method was implemented to estim ate optimum values for these parameters. The resultant optimum three-l evel time scheme produced very accurate results, satisfied physical re ality, and did not produce any oscillations for the various problems t hat were investigated. The optimum values for the two parameters beta and gamma in the three-level scheme were beta = 0.50005 and gamma = 1. 0007. A comparison was made between this optimum scheme and other exis ting three-level time schemes. The optimum scheme demonstrated superio r results for all the problems that were analysed. However, the result s of the optimization analysis produced a set of optimum parameters th at were identical to the values that would reduce the general three-le vel time scheme into a central-difference two-level time scheme, i.e. beta = 1/2 and gamma = 1.