A splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problem

Abstract

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.