Optimal solution of a reaction–diffusion system with a control discrete source term

In this paper we study the numerical behavior of a reaction–diffusion system with a control source point. The main goal consists in estimating the position of the source point that maximizes a given objective function. To reduce the number of variables involved in the optimization algorithm, we first consider the problem with a fixed source point and then, according to the numerical results obtained, we estimate an approximation to the objective function, adjusting, by least squares, a special class of functions that depend on a few number of parameters. With this procedure we obtain an effective way to define the position of the source term. Copyright © 2010 John Wiley & Sons, Ltd.