It is well known that difference schemes for hyperbolic equations display dispersion of waves. For a general dissipative difference scheme, we present a dispersive wave equation and show that the dispersions are essentially the same when the initial data is a step function.

We consider the class of viscous-dispersive and higher-order conservation laws. We generalize the work of Kawashima and Shizuta, and others, by extending to higher-order the notions of symmetrizability, strict dissipativity, and genuine coupling. We prove, for symmetrizable systems, that strict dissipativity is equivalent to both (i) genuine coupling and (ii) the existence of a skew-symmetric c...

For α ∈ (1, 2) we prove that the initial-value problem

The revenue ranking of asymmetric auctions with two heterogenous bidders is examined. The main theorem identi…es a general environment in which the …rst-price auction is more pro…table than the second-price auction. By using mechanism design techniques, the problem is simpli…ed and several extensions are made possible. Roughly speaking, the …rst-price auction is more pro…table when the strong b...

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...