Iterative identification of the spacewise-dependent right-hand side in a parabolic equation

  • Su Ling-De, sulingde@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
  • Vasil'ev Vasily I., vasvasil@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: parabolic equation, inverse problem, source identification, difference scheme, conjugate gradient method

Abstract

The problem of determining a spacewise-dependent right-hand side in a one-dimensional parabolic equation is considered. The method of conjugate gradients in combination with the method of finite differences with implicit time approximation with the weighting factor $\sigma\in[0, 1]$ is used for the numerical solution of the inverse initial-boundary value problem. The effectiveness of the proposed computational algorithm is confirmed by the results of the computational experiment for model problems with quasi-real solutions, including problems with overdetermination conditions having random errors.

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How to Cite
Su, L.-D. and Vasil’ev, V. ( ) “Iterative identification of the spacewise-dependent right-hand side in a parabolic equation”, Mathematical notes of NEFU, 26(1), pp. 81-92. doi: https://doi.org/10.25587/SVFU.2019.101.27249.
Section
Mathematical Modeling