Summary: This paper considers the problem of finding and which satisfy
in , , , is known on the boundary of and also , , where is known.
Three different finite-difference schemes are presented for identifying the control parameter , which produces, at any given time, a desired energy distribution in a portion of the spatial domain. The finite difference schemes developed for this purpose are based on the (1,5) fully explicit scheme, and the (5,5) Noye-Hayman (N-H) fully implicit technique, and the Peaceman and Rachford (P-R) alternating direction implicit (ADI) formula. These schemes are second-order accurate.
The ADI scheme and the 5-point fully explicit method use less central processor (CPU) time than the (5,5) N-H fully implicit scheme. The P-R ADI scheme and the (5,5) N-H fully implicit method have a larger range of stability than the (1,5) fully explicit technique. The results of numerical experiments are presented, and CPU times needed for this problem are reported.