DETERMINATION OF AN UNKNOWN DIFFUSION COEFFICIENT IN A PARABOLIC INVERSE PROBLEM

Authors

Keywords:

finite difference methods, parabolic inverse problem, convergence, Error estimates, maximum principle.

Abstract

In this paper we studied the finite difference scheme for the solution of one dimensional parabolic inverse problem of finding the function  and the unknown positive coefficient . The Backward time centered space (BTCS) which is unconditionally stable is studied and its convergent is proved using application of discrete maximum principle. Error estimates for  and  is studied and to give clear overview of the methodology several model problems are solved numerically. According to the experimental numerical results and the concluding remark are presented

Dimensions

Azari, H. (2002). Numerical procedures for the determination of an unknown coefficient in parabolic differential equations.

Dehghan, M. (2005). Identification of a timeâ€dependent coefficient in a partial differential equation subject to an extra measurement. Numerical Methods for Partial Differential Equations, 21(3), 611-622.

Shamsi, M., & Dehghan, M. (2007). Recovering a timeâ€dependent coefficient in a parabolic equation from overspecified boundary data using the pseudospectral Legendre method. Numerical Methods for Partial Differential Equations, 23(1), 196-210.

Rundell, W., & Colton, D. L. (1980). Determination of an unknown non-homogeneous term in a linear partial differential equation.from overspecified boundary data. Applicable Analysis, 10(3), 231-242.

Cannon, J. R., Lin, Y., & Wang, S. (1992). Determination of source parameter in parabolic equations. Meccanica, 27(2), 85-94.

Cannon, J. R., & Yin, H. M. (1990). Numerical solutions of some parabolic inverse problems. Numerical Methods for Partial Differential Equations, 6(2), 177-191.

Cannon, J. R. (1963). Determination of an unknown coefficient in a parabolic differential equation. Duke Math. J, 30(2), 313-323.

Yin, H. M. (1995). Recent and new results o determination of unknown coefficients in parabolic partial differential equations with over-specified conditions. In Inverse problems in diffusion processes: proceedings of the GAMM-SIAM Symposium (pp. 181-198).

Zhong, J.,Chen, Land Zhang, L., 2020. High throughput determination of high quality interdiffusion coefficient in metallic solid: a review. Journal of material science,55, pp.10303-10338.

Published

20-02-2022

How to Cite

DETERMINATION OF AN UNKNOWN DIFFUSION COEFFICIENT IN A PARABOLIC INVERSE PROBLEM. (2022). FUDMA JOURNAL OF SCIENCES, 5(4), 291-299. https://doi.org/10.33003/fjs-2021-0504-834

Issue

Vol. 5 No. 4 (2021): FUDMA Journal of Sciences - Vol. 5 No. 4

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

DETERMINATION OF AN UNKNOWN DIFFUSION COEFFICIENT IN A PARABOLIC INVERSE PROBLEM. (2022). FUDMA JOURNAL OF SCIENCES, 5(4), 291-299. https://doi.org/10.33003/fjs-2021-0504-834

Most read articles by the same author(s)