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Solving an inverse initial-boundary-value problem using basis function method

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Abstract

In this paper, we will first study the existence and uniqueness of the solution of an inverse initial-boundary-value problem, via an auxiliary problem. Furthermore, we propose a stable numerical approach based on the use of the solution to the auxiliary problem as a basis function for solving this problem in the presence of noisy data. Also note that the inverse problem has a unique solution, but this solution is unstable and hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method. The effectiveness of the algorithm is illustrated by numerical example.

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Damghan University, 36715-364, Damghan, Iran

    Reza Pourgholi, Amin Esfahani, Hamideh Rahimi & S. Hashem Tabasi

  2. Department of Mathematics, IME-USP, Rua do Matão 1010, Cidade Universitária, 05508-090 , São Paulo, SP, Brazil

    Amin Esfahani

Authors
  1. Reza Pourgholi
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  2. Amin Esfahani
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  3. Hamideh Rahimi
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  4. S. Hashem Tabasi
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Correspondence to Reza Pourgholi.

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Communicated by Ruben Spies.

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Pourgholi, R., Esfahani, A., Rahimi, H. et al. Solving an inverse initial-boundary-value problem using basis function method. Comp. Appl. Math. 32, 27–40 (2013). https://doi.org/10.1007/s40314-013-0005-y

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  • DOI: https://doi.org/10.1007/s40314-013-0005-y

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