An stable numerical algorithm for identifying the solution of an inverse problem

• Published in: Applied mathematics and computation Vol. 190; no. 1; pp. 231 - 236
• Main Authors: Shidfar, A., Damirchi, J., Reihani, P.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01-07-2007; Elsevier
• Subjects: Chebyshev polynomials; Exact sciences and technology; Finite differences approximation; Inverse parabolic problem; Least-squares method; Mathematical analysis; Mathematics; Measure and integration; Minimization; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Sciences and techniques of general use; Stability; Minimization; Stability; Least-squares method; Inverse parabolic problem; Chebyshev polynomials; Finite differences approximation; Solution uniqueness; Chebyshev polynomial; Algorithm; Partial differential equation; Inverse problem; Parabolic equation; Numerical analysis; Applied mathematics; Least squares method; Numerical solution; Mathematical model; Numerical stability; Finite difference method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.01.022

In this paper, we consider an inverse parabolic problem with space dependent coefficient. Mathematical model of the problem consists a parabolic equation in which the condition is unknown at the one of the boundary and to be determined from an overspecified data measured at an interior point inside the body. Uniqueness of the solution of under study inverse problem will be shown. Our concern for the numerical procedure for this inverse problem is based on a finite differences scheme. Stability conditions for numerical solution to inverse problem are stated. The approach of proposed method is approximated the unknown function by a set of Chebyshev polynomials, where the unknown set of expansion coefficients in unknown function are determined from the minimizing the least squares method. Some numerical examples will be given in the last section.