The second-order FD-TD algorithm developed by Yee has been successful in wakefield calculations. However, unphysical results can be obtained in wakefunction calculations of very short bunches. A detailed study of this problem is presented in this paper. It is found that the truncation error inherent in the secondorder Yee algorithm of standard codes is frequency dependent and is inadequate for ...

Numerov-type ODE Solvers are widely used for the numerical treatment of second order initial value problems. In this work we present a powerful and efficient symbolic code in Mathematica for the derivation of their order conditions and principal truncation error terms. The relative tree theory for such order conditions is presented along with the elements of combinatorial mathematics, partition...

This article explains a new concept concerning the integrals of SAS and their direct calculation from realistic experiments. Some new synonymous formulas for the calculation of the correlation function and its derivatives are represented. Some relations lead to a minimal truncation error and the error propagation can be investigated exactly. The fundamental idea for this is the @@exchange@@ of ...

This paper deals with the singularly perturbed boundary value problem for a linear second order differential-difference equation of the convection-diffusion type with small delay parameter. A fourth order finite difference method is developed for solving singularly perturbed differential difference equations. To handle the delay argument, we construct a special type of mesh, so that the term co...

In this paper, we consider viscoelastic flows in a rough domain (with typical roughness patterns of size ε ≪ 1). We present and rigorously justify an asymptotic expansion with respect to ε, at any order, based upon the definition of elementary problems: Oldroyd-type problems at the global scale defined on a smoothened domain and boundary-layer corrector problems. The resulting analysis guarante...

This paper is concerned with finding analytical solutions to the problems of reducing the effect of truncation error in models of resonant systems that include damping. Pointwise and spatial models of resonant systems are both considered in the paper. It is known that the truncation of an infinite-dimensional model produces errors in the zero locations and zero-frequency content of the system. ...

in this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...

The role of the operator-product expansion in QCD calculations is discussed. Approximating the two-point correlation function by several terms and assuming an upper bound on the truncation error along the euclidean ray, we consider two model situations to examine how the bound develops with increasing deflection from the euclidean ray towards the cut. We obtain explicit bounds on the truncation...

We study the calculation of complex transport coeffi­ cients x ( (o) and power spectra in terms of complex con­ tinued fractions. In particular, we establish classes of dynamical equilibrium and non-equilibrium systems for which we can obtain a posteriori bounds for the truncation error | ^ (to) — x(n)(c'J)| = c (a)) I X(w)(tu) — %(”-1)(w)| when the transport coefficient is approximated by its ...