Introduction. In this note we develop a multistep formulation of the optimized Lax-Wendroff method for hyperbolic systems. This scheme was derived by Strang [6], [7]. The present formulation extends in a natural way, the two-step formulation of Richtmyer [5] for systems in one-space variable. We summarise this case in the next section. One Space Dimension. We consider the first-order conservati...

The approximation conditions of Strang and Fix are first recalled. An elementary result on the differentiation of a finite elements approximation is proved, followed by a result by Lemarié on the differentiation of a wavelet decomposition. Daubechies’ spline example is detailed. 1 The Strang and Fix conditions 1.1 Main result The following theorem relates the approximating properties of a discr...

We study the solution of neutral delay differential equations (NDDEs) by using boundary value methods (BVMs). The BVMs require the solution of nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed to solve these linear systems. We show that if an Ak1,k2-stable BVM is used for solving an m-by-m system of NDDEs, then our pr...

In [3], we proposed a numerical regularized moment method of arbitrary order (abbreviated as NRxx method) for Boltzmann-BGK equation, which makes numerical simulation using very large number of moments possible. In this paper, we are further exploring the efficiency of NRxx method with techniques including the 2nd order HLL flux with linear reconstruction to improve spatial accuracy, the RKC sc...

We consider the solution of singular perturbation delay di erential equations (SPDDEs) by using boundary value methods (BVMs). These methods require the solution of some nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We prove that if an Ak1 ; k2 -stable BVM is used for solving a sy...

SUMMARY Strang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {e iϕ }-circulant Strang-type preconditioner.

Then Strang and Fix conditions are recalled and proved. The Strang and Fix conditions caracterize the approximating properties of a shift invariant localized operator by its ability to reconstruct polynomials. In particular, it is used to relate the number of vanishing moments of a wavelet to the order of approximation provided by the corresponding multiresolution analysis. Article [1] is gener...