  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.
