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arXiv · 2304.13177

An explicit Fourier-Klibanov method for an age-dependent tumor growth model of Gompertz type

Nguyen Thi Yen Ngoc·Vo Anh Khoa
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Abstract

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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Nguyen Thi Yen Ngoc, Vo Anh Khoa. 2023-04-25. An explicit Fourier-Klibanov method for an age-dependent tumor growth model of Gompertz type. https://arxiv.org/abs/2304.13177

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