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Recovering a moving boundary from Cauchy data in an inverse problem which arises in modeling brain tumor treatment: the (quasi)linearization idea combined with radial basis functions (RBFs) approximation

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Abstract

In this paper, the dynamical modeling and behavior analysis of the inverse boundary Stefan problem which promising the understanding of modeling brain tumor treatment, are studied. To umerical simulate these models and to overcome their difficulties such as, non-linearity, free boundary property and having a non-rectangular domain, we propose the use of a strongly meshless technique based on radial basis functions in conjunction with a (quasi)linearization algorithm. Numerical examples are given to show the good accuracy and stability of the presented method.

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Authors and Affiliations

  1. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, G.C., Iran

    A. Hajiollow, Y. Lotfi & K. Parand

  2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada

    K. Parand

  3. Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, G.C, Iran

    K. Parand, A. H. Hadian & J. A. Rad

  4. Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran

    K. Rashedi

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  1. A. Hajiollow
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  2. Y. Lotfi
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  3. K. Parand
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  4. A. H. Hadian
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  5. K. Rashedi
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  6. J. A. Rad
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Hajiollow, A., Lotfi, Y., Parand, K. et al. Recovering a moving boundary from Cauchy data in an inverse problem which arises in modeling brain tumor treatment: the (quasi)linearization idea combined with radial basis functions (RBFs) approximation. Engineering with Computers 37, 1735–1749 (2021). https://doi.org/10.1007/s00366-019-00909-8

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