We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods. 相似文献
The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above. 相似文献
Traditional ensiling of plant material by anaerobic lactic acid fermentation was combined with enzymatic hydrolysis (ENLAC for short) with cell wall degrading enzymes (hemicellulases, cellulases, and pectinases) to increase fiber digestibility or to increase the recovery of cell content from plants. Such findings were made using 0.015% (w/w, wet basis) Phylacell® enzyme preparation by ENLAC of corn and corn-sorghum mixtures, but not of forage grasses. Addition to alfalfa of a mixture of cell wall degrading enzymes, such as NOVO Viscozyme® together with NOVO Celluclast® each at 0.2–1.0% (w/w, wet basis), resulted in more rapid ensiling and improvement of rumen digestibility of silage by 20%. After 20 d of ensiling at 25 °C when the same enzymes were added to alfalfa at the 1.0% level, protein recovery by pressing increased by 35%, β-carotene recovery by 80%, and chlorophyll/xanthophyll recovery by 30%. ENLAC with the same enzymes also increased the recovery of sclareol from muscatel sage by 400%.