Numerical method for solving boundary inverse problem for one-dimensional parabolic equation

Vasily I. Vasil’ev; Ling-De Su

doi:10.25587/SVFU.2017.2.9250

Vasil’ev Vasily I., vasvasil@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42, Kulakovsky St., Yakutsk 677000, Russia
Su Ling-De, sulingde@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42, Kulakovsky St., Yakutsk 677000, Russia

DOI: https://doi.org/10.25587/SVFU.2017.2.9250

Keywords: boundary inverse problem, ﬁnite diﬀerence method, numerical solution, parabolic partial diﬀerential equation

Abstract

We consider a numerical method for solving boundary inverse problem using the implicit diﬀerence scheme for approximation by time and ﬁnite diﬀerence method for the boundary inverse problem. A numerical solution to the boundary inverse problem is determined by special decomposition which transforms the problem into two standard problems. We present the results of numerical experiments, including those with random errors in the input data, which conﬁrm the capabilities of the proposed computational algorithms for solving this boundary inverse problem.

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