Fully discrete hyperbolic initial boundary value problems with nonzero initial data

Fully discrete hyperbolic initial boundary value problems with nonzero initial data

The stability theory for hyperbolic initial boundary value problems relies most of the time on the Laplace transform with respect to the time variable. For technical reasons, this usually restricts the validity of stability estimates to the case of zero initial data. In this article, we consider the class of non-glancing finite difference approximations to the hyperbolic operator. We show that ...

Solving Discrete Initial- and Boundary-Value Problems

Multivariate linear recurrences appear in such diverse elds of mathematics as combinatorics, probability theory, and numerical resolution of partial diierential equations. Whereas in the univariate case the solution of a constant-coeecient recurrence always has a rational generating function, this is no longer true in the multivariate case where this generating function can be non-rational, non...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Initial Boundary Value Problems for Hyperbolic Partial Differential Equations

1, Differential equations in one space dimension. The simplest hyperbolic differential equation is given by (1.1) du/dt = cdu/dx, where c is a constant, Its general solution is u(x, t) — F(x + ci), i.e., it is constant along the "characteristic lines" x + ct = const (see Figure 1). Therefore, if we u(l,t) = g(t) u(0,t)*g(t want to determine the solution of (1.1) in the region 0 ^ x ^ 1, t ja 0,...

Well-posedness of hyperbolic Initial Boundary Value Problems

Assuming that a hyperbolic initial boundary value problem satsifies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The coefficients are assumed to have only finite smoothness in view of applications to nonlinear problems. This shows that the weak Lopatinskii condition is roughly sufficient to ensure well-posedness ...