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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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
25.04.2023
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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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DOI: | 10.48550/arxiv.2304.13177 |