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• W1963908997 endingPage "1942" @default.
• W1963908997 startingPage "1933" @default.
• W1963908997 abstract "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 ut=uxx+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 ∫01k(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." @default.
• W1963908997 created "2016-06-24" @default.
• W1963908997 creator A5044309986 @default.
• W1963908997 creator A5068934056 @default.
• W1963908997 date "2007-06-01" @default.
• W1963908997 modified "2023-09-24" @default.
• W1963908997 title "Identifying a control function in parabolic partial differential equations from overspecified boundary data" @default.
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• W1963908997 doi "https://doi.org/10.1016/j.camwa.2006.01.018" @default.
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