Finite difference schemes for two-dimensional parabolic inverse problem with temperature overspecification

Two different explicit finite difference schemes for solving the two-dimens ional parabolic inverse problem with temperature overspecification are cons idered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are bas ed on the second-order, 5-point Forward Time Centred Space (FTCS) explicit formula, and the (1,9) FTCS explicit scheme which is generally second-order , but is fourth order when the diffusion number takes the value s = (1/6). These schemes are economical to use, are second-order and have bounded rang e of stability. The range of stability for the 5-point formula is less rest rictive than the (1,9) FTCS explicit scheme. The results of numerical exper iments are presented, and accuracy and Central Processor (CPU) times needed for each of the methods are discussed. These schemes use less central proc essor times than the second-order fully implicit method for two-dimensional diffusion with temperature overspecification. We also give error estimates in the maximum norm for each of these methods.