A novel baseline estimation procedure building on previously published works is presented. •The core of the estimation is an iterative spectrum suppression consisting of a moving window minimum replacement (adapted from Friedrichs [1]).•Four, easily understandable, parameters control placement of the baseline relative to the noise band around the signal (adapted from Eilers [2]) and the flexibi...

We give a further examination of the stabilized Residual Distribution schemes for the solution of the shallow water equations proposed in (Ricchiuto and Bollermann, J.Comp.Phys., available online 25 October 2008). Based on a non-linear variant of a Lax-Friedrichs scheme, the scheme is wellbalanced, able to handle dry areas and, for smooth regions of the solution, obtains second order of accurac...

A generalization of the cosine of the Friedrichs angle between two subspaces to several closed subspaces in a Hilbert space is given. This is used to analyze the rate of convergence in the von Neumann-Halperin method of cyclic alternating projections. General dichotomy theorems are proved, in the Hilbert or Banach space situation, providing conditions under which the alternative QUC/ASC (quick ...

This paper is to study the asymptotic stability of stationary discrete shocks for the Lax-Friedrichs scheme approximating nonconvex scalar conservation laws, provided that the summations of the initial perturbations equal to zero. The result is proved by using a weighted energy method based on the nonconvexity. Moreover, the l1 stability is also obtained. The key points of our proofs are to cho...

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by c...

The portion of the Courant-Friedrichs-Lwy paper [Math. Ann. 100, 32 (1928)] that was devoted to hyperbolic difference equations is critically reviewed in terms of its basic contribution to the numerical solution of partial differential equations. Some subsequent developments are then discussed, including recent literature related to the von Neumann condition, some irreversible schemes, generali...

In this paper, the Cauchy problem for a Friedrichs system on globally hyperbolic manifold with timelike boundary is investigated. By imposing admissible conditions, existence and uniqueness of strong solutions are shown. Furthermore, if hyperbolic, proved to be well-posed in sense Hadamard. Finally, examples systems conditions provided.

Staggered grid finite volume methods (also called central schemes) were introduced in one dimension by Nessyahu and Tadmor in 1990 in order to avoid the necessity of having information on solutions of Riemann problems for the evaluation of numerical fluxes. We consider the general case in multidimensions and on general staggered grids which have to satisfy only an overlap assumption. We interpr...

The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability ...

We propose a simple, fast sweeping method based on the Lax–Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton–Jacobi equations in any number of spatial dimensions. By using the Lax–Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss–Seidel type nonlinear ite...