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

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.