Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis
SIAM Journal on Numerical Analysis
Maxwellian Decay for Well-balanced Approximations of a Super-characteristic Chemotaxis Model
SIAM Journal on Scientific Computing
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We investigate finite difference schemes which approximate $2\times 2$ one-dimensional linear dissipative hyperbolic systems. We show that it is possible to introduce some suitable modifications in standard upwinding schemes, which keep into account the long-time behavior of the solutions, to yield numerical approximations which are increasingly accurate for large times when computing small perturbations of stable asymptotic states, respectively, around stationary solutions and in the diffusion (Chapman-Enskog) limit.