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Numerical Solution of the Inverse Problem for the Diffusion Equation Under Spherical Symmetry

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We consider an initial–boundary-value problem for the diffusion equation with spherical symmetry and an unknown initial condition. Additional information to determine the unknown initial condition is provided by the external volume potential whose density is a Laplace operator evaluated on the solution of the initial–boundary-value problem. A numerical method is proposed for the corresponding inverse problem. Its efficiency is assessed by a computer experiment.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    S. I. Solov’eva

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  1. S. I. Solov’eva
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Correspondence to S. I. Solov’eva.

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Translated from Prikladnaya Matematika i Informatika, No. 47, 2014, pp. 77–81.

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Solov’eva, S.I. Numerical Solution of the Inverse Problem for the Diffusion Equation Under Spherical Symmetry. Comput Math Model 26, 528–533 (2015). https://doi.org/10.1007/s10598-015-9289-7

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  • DOI: https://doi.org/10.1007/s10598-015-9289-7

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