One of the global approaches for solving the two dimensional inverse parabolic problem
is the predictor corrector which takes place for evaluating the pair (u,p) and adjusting
the evaluation for the desired accuracy. For general class of higher dimensional
parabolic problems the ADI or the FS methods have been considered with an advantage
of reducing or splitting the problem, in accordance to the time fractions, into one
dimensional dependent problems and they are a non-parallel type of splittings. In
1992 Lu et al. proposed an additive parallel type of splitting method such that the splitting
is defined in accordance to the spatial variables to solve multi dimensional parabolic
problem.
In this work we will present a new algorithm for solving two or higher dimensional
inverse control problem. The algorithm is a parallel predictor corrector type of method
such that the solution and the predictor and corrector schemes are defined by the parallel
splitting up method. Some numerical results from the solution of two model problems
are considered to demonstrate the accuracy of the presented algorithm.
