Determination of a control function in three-dimensional parabolic equations
In: Mathematics and computers in simulation, Jg. 61 (2003), Heft 2, S. 89-100
Online
academicJournal
- print, 20 ref
This study presents numerical schemes for solving two three-dimensional parabolic inverse problems. These schemes are developed for indentifying the parameter p(t) which satisfy ut = uxx + uyy + uzz + p(t)u + Φ, in R×(0, T], u(x, y, z, 0) = f(x, y, z), (x, y, z) E R = [0, 1]3. It is assumed that u is known on the boundary of R and subject to the integral overspecification over a portion of the spatial domain ∫10 ∫10 ∫10 u(x, y, z, t)dx dy dz = E(t), 0 ≤ t ≤ T, or to the overspecification at a point in the spatial domain u(x0, y0, z0, t) = E(t), 0 ≤ t ≤ T, where E(t) is known and (x0, y0, z0) is a given point of R. These schemes are considered for determining the control parameter which produces, at any given time, a desired energy distribution in the spacial domain, or a desired temperature distribution at a given point in the spacial domain. A generalization of the well-known, explicit Euler finite difference technique is used to compute the solution. This method has second-order accuracy with respect to the space variables. The results of numerical experiments are presented and the accuracy and the central processor (CPU) times needed are reported.
Titel: |
Determination of a control function in three-dimensional parabolic equations
|
---|---|
Autor/in / Beteiligte Person: | DEHGHAN, Mehdi |
Link: | |
Zeitschrift: | Mathematics and computers in simulation, Jg. 61 (2003), Heft 2, S. 89-100 |
Veröffentlichung: | Amsterdam: Elsevier, 2003 |
Medientyp: | academicJournal |
Umfang: | print, 20 ref |
ISSN: | 0378-4754 (print) |
Schlagwort: |
|
Sonstiges: |
|