In this paper, the origins of spurious solutions occurring in the high-order finite difference methods are studied. Based on a uniform mesh, spurious modes are found in the high-order one-sided finite difference discretizations of many eigenvalue problems. Spurious modes are classified as spectral pollution and non-spectral pollution. The latter can be partially avoided by mesh refinement, whil...

A compact two-dimensional (2-D) full-wave finite-difference frequency-domain method is proposed for the analysis of dispersion characteristics of a general guided wave structure. Because the longitudinal field components are eliminated in the proposed method, only four transverse field components are involved in the final resulting eigen equation. This feature considerably reduces the required ...

Electrochemical systems are considered for which the concentration of ions in solution is low, and therefore there is an electric field which extends deep into solution away from the electrode surface. Finite difference methods are used to model a potential step chronoamperometry experiment at a microhemisphere electrode. Concentration profiles, potential profiles, and current-time curves are p...

Pott has shown that the product of two semiregular relative difference sets in commuting groups El and E2 relative to their intersection subgroup C is itself a semiregular relative difference set in their amalgamated direct product. We generalise this result in the case that C is central in El and in E2 by using an equivalence with corresponding co cycles 7./Jl and 'l/J2' We prove that in the c...

Larix chinensis Beissn., as a native, dominant and climate-sensitive coniferous species at Mount Taibai timberline, Qinling mountains, is rarely disturbed by anthropogenic activities; thus, it an ideal proxy for the investigation of climate change or vegetation evolution. In this study, we applied dendrochronological methods to L. tree-ring series from Mt. investigated relationships between wid...

Abstract Let $$C(\lambda )\subset [0,1]$$ C ( ? ) ? [ 0 , 1 ] denote the central Cantor set generated by a sequence $$\lambda =(\lambd...