Volume 1: Issue 1

Volume 1: Issue 1

A note from the Editor in Chief

Every new day comes with a new hope, and so it seems appropriate to start our first issue with a brief letter to announce the establishment of Online Mathematics Journal (OMJ). We have launched this journal as a nonprofit open-access platform to create a fast and convenient opportunity of publication, for any noteworthy research in the field of mathematics. Our main goal is to provide students, researchers, and academicians with a free and high-quality publication service, so as to promote their latest findings, and to stimulate research in the field of mathematics, by supporting and funding their bright ideas.

Moreover, we strive to ease international scientific communications in the field of mathematics, by gathering cutting-edge scientific findings in most sub-fields of mathematics and creating a quality environment for researchers, to exchange their knowledge.

Online Mathematics Journal

Reviewing the linearized compact difference scheme for a one-dimensional parabolic inverse problem

Author(s):  Areen Al-Khateeb, Asma Amani
Keywords :  Inverse Parabolic Problem, Control Parameters, Linearized Compact Scheme, Difference Scheme
Refer this article:  A. Al-Khateeb, A. Amani, Reviewing the linearized compact difference scheme for a one-dimensional parabolic inverse problem, Online Mathematics Journal. 1 (1) (2019) 4-13.

This paper investigates the numerical method for a one-dimensional parabolic inverse problem that was developed by Chao-Rong and Zhi-Zhong (2009). The cretization accuracy and convergence of the developed model is calculated and the existence of solutions with inverse boundary conditions is proven. Furthermore, results are compared to previous findings in terms of computational costs and indicate an improvement in both computational efficiency and accuracy.

[1] J.R. Cannon, Y.L. Lin, S. Xu, Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations, Inverse Probl., 10 (1994), pp. 227-243

[2] M. Dehghan, Finding a control parameter in one-dimensional parabolic equations, Appl. Math. Comput., 135 (2003), pp. 491-503

[3] D.S. Daoud, D. Subasi, A splitting up algorithm for the determination of the control parameter in multidimensional parabolic problem, Appl. Math. Comput., 166 (2005), pp. 584-595

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