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1.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
2.
WANG Libin 《数学年刊B辑(英文版)》2002,23(4):439-454
The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension. 相似文献
3.
D. Yafaev 《Proceedings Mathematical Sciences》2002,112(1):245-255
We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover,
the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables.
This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday. 相似文献
4.
R. Uribe-Vargas 《Functional Analysis and Its Applications》2003,37(3):236-240
On a smooth surface in Euclidean 3-space, we consider vanishing curves whose projections on a given plane are small circles centered at the origin. The bifurcations diagram of a parameter-dependent surface is the set of parameters and radii of the circles corresponding to curves with degenerate flattening points. Solving a problem due to Arnold, we find a normal form of the first nontrivial example of a flattening bifurcation diagram, which contains one continuous invariant. 相似文献
5.
The 11 800-14 380 cm−1 frequency range has been scanned for rotationally resolved rovibronic transitions in the A2B2-X2A1 electronic band system of the symmetric (C2v) 16O14N16O and 18O14N18O isotopologues and in the corresponding electronic band system of the asymmetric (Cs) 18O14N16O isotopologue. The rotational analysis—reflecting minor differences in mass—in combination with symmetry induced spectral differences allows an identification of 68 16O14N16O vibronic levels, 26 18O14N18O vibronic levels and 51 18O14N16O vibronic levels. The bands are recorded using near infrared fluorescence spectroscopy and a piezo valve based pulsed molecular beam expansion of premixed 18O2 and 14N16O in Ar. The majority of the observed bands is rotationally assigned and can be identified as transitions starting from the vibrational ground state of one of the isotopologues. Numerous hot bands have also been identified. A comparison of the overall spectroscopic features of C2v vs. Cs symmetric species provides qualitative information on symmetry dependence of vibronic couplings. 相似文献
6.
考虑具常数特征拟线性双曲型方程,提出一个新的可化约方程组的方法,证明了具常特征方程组Cauchy问题经典解的整体存在性定理.同时构造一些例子说明一些有趣的现象. 相似文献
7.
8.
The quality of the surface of metallic wires is relevant for different applications. The reflection of a laser beam on the surface of a metallic cylindrical wire provides an efficient way to inspect the quality of its surface. Our interest is focused in the detection of axially oriented defects, which are the most relevant for the wire drawing process. We present a simple interference-geometrical model to describe the light pattern reflected from a wire with defects. This model adequately accounts for the observed results from an industrial prototype developed for the purpose. It incorporates three-laser beams incident on the wire at equidistant locations in its perimeter, which produce three reflection cones with a CCD. This configuration permits to explore the whole perimeter of the wire. Several results are presented, both in static operation and in production line, in agreement with qualitative and quantitative predictions. 相似文献
9.
We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII0, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII0 cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII0 cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime. 相似文献
10.
Pedro J. Torres 《Journal of Differential Equations》2007,232(1):277-284
In a periodically forced semilinear differential equation with a singular nonlinearity, a weak force condition enables the achievement of new existence criteria through a basic application of Schauder's fixed point theorem. The originality of the arguments relies in that, contrary to the customary situation in the available references, a weak singularity facilitates the arguments of the proofs. 相似文献