Author： Cai Wenli Liu Hailiang
Publisher： Edp Sciences
E-ISSN： 1290-3841|51|4|1223-1243
ISSN： 0764-583x
Source： ESAIM: Mathematical Modelling and Numerical Analysis, Vol.51, Iss.4, 2017-06, pp. : 1223-1243
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
In this paper, we design, analyze and numerically validate energy dissipating finite volume schemes for a competition-mutation equation with a gradient flow structure. The model describes the evolution of a population structured with respect to a continuous trait. Both semi-discrete and fully discrete schemes are demonstrated to satisfy the two desired properties: positivity of numerical solutions and energy dissipation. These ensure that the positive steady state is asymptotically stable. Moreover, the discrete steady state is proven to be the same as the minimizer of a discrete energy function. As a comparison, the positive steady state can also be produced by a nonlinear programming solver. Finally, a series of numerical tests is provided to demonstrate both accuracy and the energy dissipation property of the numerical schemes. The numerical solutions of the model with small mutation are shown to be close to those of the corresponding model with linear competition.
Related content
Access to resources
Recommend
