Identifying a control function in parabolic partial differential equations from overspecified boundary data

• Authors: Mehdi Tatari;Mehdi Dehghan
• Venue: Computers & Mathematics with Applications
• Year: 2007

Determination of an unknown time-dependent function in parabolic partial differential equations, plays a very important role in many branches of science and engineering. In the current investigation, the Adomian decomposition method is used for finding a control parameter p(t) in the quasilinear parabolic equation u"t=u"x"x+p(t)u+@f, in [0,1]x(0,T] with known initial and boundary conditions and subject to an additional condition in the form of @!"0^1k(x)u(x,t)dx=E(t),0@?t@?T which is called the boundary integral overspecification. The main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known Adomian decomposition method. The decomposition procedure of Adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form. Furthermore due to the rapid convergence of Adomian's method, a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution. This method provides a reliable algorithm that requires less work if compared with the traditional techniques. Some illustrative examples are presented to show the efficiency of the presented method.