Now showing items 1-6 of 6
Dispersion for 1-d Schrödinger and wave equations with bv coefficients
In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ...
Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are ...
Asymptotic expansions for anisotropic heat kernels
We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity ...
Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrödinger equations on the real line. Recently, the authors have introduced viscous and ...
Numerical dispersive schemes for the nonlinear Schrödinger equation
We consider semidiscrete approximation schemes for the linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model hold for these approximations. For the conservative finite ...
Convergence of a two-grid algorithm for the control of the wave equation
We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square.We prove the uniform (with respect to the meshsize) boundary observability for the ...