TY - JOUR
ID - 277
TI - Parameter determination in a parabolic inverse problem in general dimensions
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Zolfaghari, Reza
AD - Salman Farsi University of Kazerun
Y1 - 2013
PY - 2013
VL - 1
IS - 1
SP - 55
EP - 70
DO -
N2 - It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse problem to a Volterra integral equation of convolution-type. By using an explicit procedure based on Sinc function properties, the resulting integral equation is replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number and the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some numerical examples are given to demonstrate the computational efficiency of the method.
UR - https://cmde.tabrizu.ac.ir/article_277.html
L1 - https://cmde.tabrizu.ac.ir/article_277_64be06a89a3e7813e006630e885ee04c.pdf
ER -