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Advances in Applied Mathematics and Mechanics 2012年第1期4卷 1-20页

作者： Yunxia Wei Yanping Chen School of Mathematics and Computational Science Sun Yat-sen UniversityGuangzhou 510275China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel(t−s)^(−μ) with 0<μ<*** this work,we consider the case when the underlying soluti... 详细信息

The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel(t−s)^(−μ) with 0spectral methods,which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-*** numerical examples are given to illustrate the theoretical results.

关键词： ∞Volterra integro-differential equations weakly singular kernels spectral methods convergence analysis

On the efficiency of semi-implicit and semi-Lagrangian spectral methods for the calculation of incompressible flows

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On the efficiency of semi-implicit and semi-Lagrangian spect...

Super-Fast Approximation Algorithms Using Classical Fourier Tools

中国空气动力学学会第十届物理气体动力学专业委员会会议

作者： Richard PASQUETTI Laboratoire J. A. Dieudonne UMR CNRS 6621 UNSA 06108 Nice France

＜正＞Classical semi-implicit Backward-Euler/Adams-Bashforth time-discretizations of the Navier-Stokes equations induce, for high Reynoldsnumber flows, severe restrictions on the time step. Such restrictionscan be relaxed by using semi-Lagrangian schemes, essentially based onthe splitting of the full problem into an explicit transport step and animplicit diffusion step. In comparison with the standard characteristicsmethod, the semi-Lagrangian method has the advantage to be muchless CPU-time consuming when spectral methods are concerned. Thepaper is devoted to the comparison of the "semi-implicit" and "semi-Lagrangian" approaches, in terms of stability, accuracy and computa-tional efficiency. Numerical results on the advection equation, Burger’sequation and finally 2D and 3D Navier-Stokes equations, using spectralelements or a collocation method, are provided.

关键词： Navier-Stokes equations spectral methods High Reynolds number flows Characteristics method Semi-Lagrangian methods.

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Advances in Pure Mathematics 2024年第7期14卷 596-618页

作者： Anry Nersessian Institute of Mathematics National Academy of Sciences of the Republic of Armenia Yerevan Armenia

In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered that knowledge of a finite number of Fourier coefficients of function f from an infinite-dimensional set of elementary functions allows f to be accurately restored (the phenomenon of over-convergence). Below, parametric biorthogonal systems are constructed for classical trigonometric Fourier series, and the corresponding phenomena of over-convergence are discovered. The decisive role here was played by representing the space L2 as an orthogonal sum of two corresponding subspaces. As a result, fast parallel algorithms for reconstructing a function from its truncated trigonometric Fourier series are proposed. The presented numerical experiments confirm the high efficiency of these convergence accelerations for smooth functions. In conclusion, the main results of the work are summarized, and some prospects for the development and generalization of the proposed approaches are discussed.

关键词： Fourier Series Acceleration of Convergence Parametric Biorthogonalization spectral methods Over-Convergence Phenomenon

ON THE ERROR ESTIMATES FOR THE ROTATIONAL PRESSURE-CORRECTION PROJECTION spectralmethods FOR THE UNSTEADY STOKES EQUATIONS

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Journal of Computational Mathematics 2005年第3期23卷 285-304页

作者： Feng-huiHuang DepartmentofMathematics XiamenUniversityXiamen361005China

This paper provides an analysis of the rotational form of the pressure-correction methods by spectral approximations for the unsteady Stokes equations. Error estimates in finite time for the fully discrete case are given. Numerical experiences using both spectral and spectral element methods are carried out to confirm the theoretical results.

关键词： Stokes equations Projection methods spectral methods

Insight into the interaction between trimethoprim and soluble microbial products produced from biological wastewater treatment processes

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Journal of Environmental Sciences 2023年第2期124卷 130-138页

作者： Runze Xu Fang Fang Longfei Wang Jingyang Luo Jiashun Cao Key Laboratory of Integrated Regulation and Resource Development on Shallow Lakes Ministry of EducationCollege of EnvironmentHohai UniversityNanjing 210098China

Soluble microbial products(SMPs),dissolved organic matter excreted by activated sludge,can interact with antibiotics in wastewater and natural water *** between SMPs and antibiotics can influence antibiotic migration,transformation,and toxicity but the mechanisms involved in such interactions are not fully *** this study,integrated spectroscopy approaches were used to investigate the mechanisms involved in interactions between SMPs and a representative antibiotic,trimethoprim(TMP),which has a low biodegradation rate and has been detected in *** results of liquid chromatography-organic carbon detection-organic nitrogen detection indicated that the SMPs used in the study contained 15% biopolymers and 28% humic-like substances(based on the total dissolved organic carbon concentration)so would have contained sites that could interact with TMP.A linear relationship of fluorescent intensities of tryptophan protein-like substances in SMP was observed(R^(2)>0.99),indicating that the fluorescence enhancement between SMP and TMP ***-transform infrared spectroscopy and X-ray photoelectron spectroscopy indicated that carboxyl,carbonyl,and hydroxyl groups were the main functional groups involved in the *** electrostatic andπ-πinteractions were discovered by the UV-vis spectra and 1H nuclear magnetic resonance *** representations of the interactions between representative SMP subcomponents and TMP were calculated using density functional theory,and the results confirmed the conclusions drawn from the 1H nuclear magnetic resonance *** results help characterize SMP–TMP complexes and will help understand antibiotic transformations in wastewater treatment plants and aquatic environments.

关键词： Activated sludge process Interaction mechanism Antibiotics Soluble microbial products(SMP) spectral methods

Fast Numerical methods for Stochastic Computations:A Review

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Communications in Computational Physics 2009年第2期5卷 242-272页

作者： Dongbin Xiu Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA

This paper presents a review of the current state-of-the-art of numerical methods for stochastic *** focus is on efficient high-order methods suitable for practical applications,with a particular emphasis on those based on generalized polynomial chaos(gPC)*** framework of gPC is reviewed,along with its Galerkin and collocation approaches for solving stochastic *** of these methods are summarized by using results from *** paper also attempts to present the gPC based methods in a unified framework based on an extension of the classical spectral methods into multi-dimensional random spaces.

关键词： Stochastic differential equations generalized polynomial chaos uncertainty quantification spectral methods

THE LARGE TIME BEHAVIOR OF spectral APPROXIMATION FOR A CLASS OF PSEUDOPARABOLIC VISCOUS DIFFUSION EQUATION

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Acta Mathematica Scientia 2007年第1期27卷 153-168页

作者：尚亚东 School of Mathematics and Information Science Guangzhou University

The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.

关键词： Pseudoparabolic diffusion equation viscosity spectral methods long time behavior large time error estimates

Isolation and Crystal Structure of Trans-2,2',4,4'-tetramethyl-6,6'-dinitro Azobenzene

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Chinese Journal of Structural Chemistry 2004年第9期23卷 1005-1008页

作者： WANG Xiao-Ling YANG Bo-Lun LI Zong-Xiao YUAN Chun-Lan YU Kai-Bei Environmental and Chemical Engineering Institute Xian Jiaotong UniversityXi'an 710049China Department of Chemistry and Chemical Engineering Baoji College of Arts and SciencesBaoji 721007China Chengdu Institute of Organic Chemistry The Chinese Academy of SciencesChengdu 610041China

Trans-2,2?,4,4?-tetramethyl-6,6?-dinitro azobenzene (C16H16N4O4, Mr = 328.32) was isolated from benzene extract of the leaves of Aconitum sungpanense Hand. Mazz. as a new compound, and characterized by spectral methods and X-ray diffraction analysis. It crystallizes in monoclinic system, space group P21/c with a = 8.544(1), b = 13.997(2), c = 7.161(1) ? ?= 112.97(1), V = 788.4(2) ?, Z = 4, Dc = 1.383 g/cm3, F(000) = 344 and ?MoKa) = 0.102 mm-1. The final R = 0.0395 and wR = 0.1140 for 1913 independent reflections with Rint = 0.0109 and 1329 observed reflections with I > 2s(I). The molecule is composed of two phenyl rings through trans N=N.

关键词： trans-2,2′,4,4′-tetramethyl-6,6′-dinitro azobenzene aconitum sungpanense Hand.Mazz. spectral methods X-ray diffraction analysis

Ice-Induced Fatigue Analysis by spectral Approach for Offshore Jacket Platforms with Ice-Breaking Cones

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China Ocean Engineering 2007年第1期21卷 1-10页

作者：岳前进刘圆张日向屈衍王瑞学 State Key Laboratory of Structural Analysis of Industrial Equipment Dalian University of Technology School of Civil and Hydraulic Engineering Dalian University of Technology

The spectral methods and ice-induced fatigue analysis are discussed based on Miner＇s linear cumulative fatigue hypothesis and S-N curve data. According to the long-term data of full-scale tests on the platforms in the Bohai Sea, the ice force spectrum of conical structures and the fatigue environmental model are established. Moreover, the finite element model of JZ20-2MSW platform, an example of ice-induced fatigue analysis, is built with ANSYS software. The mode analysis and dynamic analysis in frequency domain under all kinds of ice fatigue work conditions are carded on, and the fatigue life of the structure is estimated in detail. The methods in this paper can be helpful in ice-induced fatigue analysis of ice-resistant platforms.

关键词： ice-resistant platform spectral methods ice force spectrum fatigue analysis

Explicit Shifted Second-kind Chebyshev spectral Treatment for Fractional Riccati Differential Equation

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Computer Modeling in Engineering & Sciences 2019年第12期121卷 1029-1049页

作者： W.M.Abd-Elhameed Y.H.Youssri Department of Mathematics Faculty of ScienceUniversity of JeddahJeddahSaudi Arabia Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt

This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is *** formula is expressed in terms of a certain terminating hypergeometric function of the type_(4)F_(3)(1).This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3 F 2(1)which can be summed with the aid of Watson’s *** illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.

关键词： Chebyshev polynomials of the second kind spectral methods linearization formula hypergeometric functions