Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions

@article{Liu2015EntropySS,
title={Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions},
author={H. Liu and W. Cai and N. Su},
journal={SIAM J. Numer. Anal.},
year={2015},
volume={53},
pages={1393-1417}
}

In this paper, we present entropy satisfying schemes for solving an integro-differential equation that describes the evolution of a population structured with respect to a continuous trait. In [P.-E. Jabin and G. Raoul, J. Math. Biol., 63 (2011), pp. 493--517] solutions are shown to converge toward the so-called evolutionary stable distribution (ESD) as time becomes large, using the relative entropy. At the discrete level, the ESD is shown to be the solution to a quadratic programming problem… CONTINUE READING