A finite chain calculation in terms of Hubbard X-operators is explored by setting up a vibronic Harniltonian. The model conveniently transformed into a form so that in the case of strong coupling a numerical renormalization group approach is applicable. To test the technique, a one particle Green function is calculated for the model Harniltonian

The pointwise error of a finite-difference calculation of supersonic flow is considered. The local truncation error is determined using a Taylor series with the remainder being in a Lagrange form. The contribution of the local truncation error to the total pointwise approximation error is estimated via adjoint parameters. It is demonstrated by numerical tests that the results of numerical calcu...

The pointwise error of a finite-difference calculation of supersonic flow is discussed. The local truncation error is determined by a Taylor series with the remainder being in a Lagrange form. The contribution of the local truncation error to the total pointwise approximation error is estimated via adjoint parameters. It is demonstrated by numerical tests that the results of the numerical calcu...

Numerical computation of textile permeability is important for composite manufacturing. Using Darcy’s law, permeability can be derived from a simulation of the fluid flow, i.e. after solving the Stokes, Navier-Stokes or Brinkman equations. The latter allow to model intra-yarn flow in case of permeable yarns. In this paper we present a numerical method for the calculation of the permeability of ...

Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and u...

Periodic travelling waves (wavetrains) are an important solution type for many partial differential equations. In this paper I review the use of numerical continuation for studying these solutions. I discuss the calculation of the form and stability of a given periodic travelling wave, and the calculation of boundaries in a two-dimensional parameter plane for wave existence and stability. I als...

We present a nonperturbative numerical evaluation of the one-photon electron self energy for hydrogenlike ions with low nuclear charge numbers Z = 1 to 5. Our calculation for the 1S state has a numerical uncertainty of 0.8 Hz for hydrogen and 13 Hz for singly-ionized helium. Resummation and convergence acceleration techniques that reduce the computer time by about three orders of magnitude were...