A uniformly converging scheme for fractal conservation laws
نویسندگان
چکیده
The fractal conservation law ∂tu + ∂x( f (u)) + (−∆)α/2u = 0 changes characteristics as α → 2 from non-local and weakly diffusive to local and strongly diffusive. In this paper we present a corrected finite difference quadrature method for (−∆)α/2 with α ∈ [0,2], combined with usual finite volume methods for the hyperbolic term, that automatically adjusts to this change and is uniformly convergent with respect to α ∈ [η ,2] for any η > 0. We provide numerical results which illustrate this asymptotic-preserving property as well as the non-uniformity of previous finite difference or finite volume type of methods.
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