Discontinuous Galerkin method for a nonlinear age-structured tumor cell population model with proliferating and quiescent phases

Dipty Sharma () and Paramjeet Singh
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Dipty Sharma: School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, India
Paramjeet Singh: School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, India

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 03, 1-18

Abstract: We propose a nonlinear age-structured model of tumor cell population with proliferating and quiescent phases. We apply the discontinuous Galerkin (DG) method to study its dynamical behavior. The DG numerical approximation is used for the spatial discretization and then the strong-stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. This paper aims to establish more efficient results in the sense of computational approach and compare these with analogous estimates for Weighted Essentially and Non-Oscillatory (WENO) scheme. Finally, some test examples and numerical simulations are given to illustrate theoretical results and to examine the behavior of the solution.

Keywords: Population dynamics; age-structured model; Lotka–McKendrick equation; discontinuous Galerkin method (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S012918312150039X

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