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

✍ Scribed by Mehdi Tatari; Mehdi Dehghan

• Book ID: 104007763
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 367 KB
• Volume: 53
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2006.01.018

✦ Synopsis

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 + φ, in [0, 1] × (0, T ] with known initial and boundary conditions and subject to an additional condition in the form of 1 0 k(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.