An explicit Fourier-Klibanov method for an age-dependent tumor growth model of Gompertz type
This paper proposes an explicit Fourier-Klibanov method as a new approximation technique for an age-dependent population PDE of Gompertz type in modeling the evolution of tumor density in a brain tissue. Through suitable nonlinear and linear transformations, the Gompertz model of interest is transfo...
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Published in | Applied numerical mathematics Vol. 198; pp. 401 - 418 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.04.2024
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Subjects | |
Online Access | Get full text |
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Summary: | This paper proposes an explicit Fourier-Klibanov method as a new approximation technique for an age-dependent population PDE of Gompertz type in modeling the evolution of tumor density in a brain tissue. Through suitable nonlinear and linear transformations, the Gompertz model of interest is transformed into an auxiliary third-order nonlinear PDE. Then, a coupled transport-like PDE system is obtained via an application of the Fourier-Klibanov method, and, thereby, is approximated by the explicit finite difference operators of characteristics. The stability of the resulting difference scheme is analyzed under the standard 2-norm topology. Finally, we present some computational results to demonstrate the effectiveness of the proposed method. |
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ISSN: | 0168-9274 1873-5460 |
DOI: | 10.1016/j.apnum.2024.01.020 |