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Numerical Solution to Inverse Problems of Recovering Special-Type Source of a Parabolic Equation

In: Mathematical Analysis in Interdisciplinary Research

Author

Listed:
  • K. R. Aida-zade

    (Institute of Control Systems of Azerbaijan NAS
    Institute of Control Systems of Azerbaijan NAS)

  • A. B. Rahimov

    (Institute of Control Systems of Azerbaijan NAS)

Abstract

The chapter investigates inverse problems of recovering a source of a special type of parabolic equation with initial and boundary conditions. The specificity of these problems is that the identifiable parameters depend on only space or time variable and are factors of the coefficients of the right-hand side of the equation. By applying the method of lines, the problems are reduced to parametric inverse problems with respect to ordinary differential equations. A special type of representation of the solution is proposed to solve them. The most important in this work is that the proposed approach to the numerical solution to the investigated inverse problems of identifying the coefficients does not require to construct any iterative procedure. The results of numerical experiments conducted on test problems are provided.

Suggested Citation

  • K. R. Aida-zade & A. B. Rahimov, 2021. "Numerical Solution to Inverse Problems of Recovering Special-Type Source of a Parabolic Equation," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 85-100, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84721-0_6
    DOI: 10.1007/978-3-030-84721-0_6
    as

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