In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence...In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.展开更多
This paper,through mass spectrometric(MS)analysis for nitro compound explosives on a direct analysis in a real‑time time‑of‑flight MS,indicates that even on a high‑resolution MS with accurate mass measurement capabili...This paper,through mass spectrometric(MS)analysis for nitro compound explosives on a direct analysis in a real‑time time‑of‑flight MS,indicates that even on a high‑resolution MS with accurate mass measurement capabilities,there is no guarantee to obtain the unique molecular formula of a compound.By calculating spectra accuracy,highly accurate isotope pattern matching can be conducted to significantly improve performance of compound confirmation or identification.展开更多
We introduce a family of orthogonal functions,termed as generalized Slepian functions(GSFs),closely related to the time-frequency concentration problem on a unit disk in D.Slepian[19].These functions form a complete o...We introduce a family of orthogonal functions,termed as generalized Slepian functions(GSFs),closely related to the time-frequency concentration problem on a unit disk in D.Slepian[19].These functions form a complete orthogonal system in L_(ωα)^(2)(−1,1)with̟ω_(α)(x)=(1−x)^(α),α>−1,and can be viewed as a generalization of the Jacobi polynomials with parameter(α,0).We present various analytic and asymptotic properties of GSFs,and study spectral approximations by such functions.展开更多
We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interf...We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space.We analyze the singular behavior of the integrals(single-layer and double-layer integrals)appearing in the equations.The interfaces are formulated in the tangent angle and arc-length coordinates and,to reduce the stiffness of the evolution equation,the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces.Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.展开更多
Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spect...Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spectral accuracy. The numerical results coincide with those of the theoretical analysis. It is easy to generalize the proposed methods to multiple-dimensional prob- lems.展开更多
文摘In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.
文摘This paper,through mass spectrometric(MS)analysis for nitro compound explosives on a direct analysis in a real‑time time‑of‑flight MS,indicates that even on a high‑resolution MS with accurate mass measurement capabilities,there is no guarantee to obtain the unique molecular formula of a compound.By calculating spectra accuracy,highly accurate isotope pattern matching can be conducted to significantly improve performance of compound confirmation or identification.
基金supported by Singapore AcRF Tier 1 Grant RG58/08,Singapore MOE Grant T207B2202Singapore NRF2007IDM-IDM002-010.
文摘We introduce a family of orthogonal functions,termed as generalized Slepian functions(GSFs),closely related to the time-frequency concentration problem on a unit disk in D.Slepian[19].These functions form a complete orthogonal system in L_(ωα)^(2)(−1,1)with̟ω_(α)(x)=(1−x)^(α),α>−1,and can be viewed as a generalization of the Jacobi polynomials with parameter(α,0).We present various analytic and asymptotic properties of GSFs,and study spectral approximations by such functions.
基金supported by the grants NSF-DMS 0511411,0914923 and 0923111.
文摘We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space.We analyze the singular behavior of the integrals(single-layer and double-layer integrals)appearing in the equations.The interfaces are formulated in the tangent angle and arc-length coordinates and,to reduce the stiffness of the evolution equation,the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces.Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.
基金the Chinese Key project on Basic Research (No.1999032804), and Shanghai Natural Science Foundation (No.00JC14D57).
文摘Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spectral accuracy. The numerical results coincide with those of the theoretical analysis. It is easy to generalize the proposed methods to multiple-dimensional prob- lems.
