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 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.