Abstract
In this paper a numerical method consists of combining Haar basis method and Tikhonov regularization method for solving some ill-posed inverse problems using noisy data is presented. By using a sensor located at a point inside the body and measuring the u(x, t) at a point x = a, 0 < a < 1, and applying Haar basis method to the inverse problem, we determine a stable numerical solution to this problem. Results show that an excellent estimation on the unknown functions of the inverse problem can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.
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Pourgholi, R., Tavallaie, N. & Foadian, S. Applications of Haar basis method for solving some ill-posed inverse problems. J Math Chem 50, 2317–2337 (2012). https://doi.org/10.1007/s10910-012-0036-4
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DOI: https://doi.org/10.1007/s10910-012-0036-4