IDENTIFICATION OF TWO PARAMETERS IN AN ELLIPTIC BOUNDARY VALUE PROBLEM

Abir Benyoucef; Leila Alem; Lahcène Chorfi

Abir Benyoucef Applied Mathematics Laboratory, Badji Mokhtar University, P.O.Box 12, Annaba 23000, Algeria
Leila Alem Applied Mathematics Laboratory, Badji Mokhtar University, P.O.Box 12, Annaba 23000, Algeria
Lahcène Chorfi Applied Mathematics Laboratory, Badji Mokhtar University, P.O.Box 12, Annaba 23000, Algeria

Article ID: 2553

Keywords: inverse problem; least squares method; Levenberg-Marquardt algorithm

Abstract

This paper concerns an inverse problem which consists in determining two coefficients b and c in the equation -b(x)u"+c(x)u'= f,x ∈]0,1[, knowing the solution function u and the right-hand side function f.The questions of uniqueness and stability are investigated. This problem is solved by using the nonlinear least squares method. We present some numerical examples to illustrate our algorithm.

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