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Acta Mathematica Sinica,English Series 2018年第10期34卷 1563-1577页

作者： Valerii IVANOV Alexey IVANOV Department of Applied Mathematics and Computer Science Tula State University

We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson＇s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.

关键词： Best approximation generalized modulus of continuity Jackson＇s inequality optimal argument Logan＇s problem quadrature formula

GENERALIZED GAUSSIAN quadrature formulaSWITH CHEBYSHEV NODES

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Journal of Computational Mathematics 1999年第2期17卷 171-178页

作者： Ying-guang Shi(ICMSEC, Chinese Academy of Sciences, Beijing 100080, China) 中科院计算数学与科学工程计算所北京

Explicit expressions of the Cotes numbers of the generalized Gaussian quadrature formulas for the Chebyshev nodes (of the first kind and the second kind) and their asymptotic behavior are given.

关键词： quadrature formula Chebyshev polynomials

Space Discretization of Time-Fractional Telegraph Equation with Mamadu-Njoseh Basis Functions

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Applied Mathematics 2022年第9期13卷 760-773页

作者： Ebimene James Mamadu Ignatius Nkonyeasua Njoseh Henrietta Ify Ojarikre Department of Mathematics Delta State University Abraka Nigeria

In this paper, we examine the space discretization of time fractional telegraph equation (TFTE) with Mamadu-Njoseh orthogonal basis functions. For ease and convenience, we deal with the fractional derivative by first converting from Caputo’s type to Riemann-Liouville’s type. The proposed method was constrained to precise error analysis to establish the accuracy of the method. Numerical experimentation was implemented with the aid of MAPLE 18 to show convergence of the method as compared with the analytic solution.

关键词： Finite Difference Method Mamadu-Njoseh Polynomials Telegraph Equation Gaussian Elimination Method quadrature formula Sobolev Space

Generalized Gaussian quadrature formulas Based on Chebyshev Nodes with Explicit Coefficients

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Chinese Quarterly Journal of Mathematics 2011年第2期26卷 300-305页

作者： CAO Li-hua ZHAO Yi College of Mathematics and Computational Science Shenzhen University Shenzhen 518060 China

The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind,and those of the(n-1)st Chebyshev polynomial of the second kind.Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences,which was proposed in[14].

关键词： quadrature formula expansions of divided diffierences Chebyshev nodes

The Maximum Trigonometric Degrees of quadrature formulae with Prescribed Nodes

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Communications in Mathematical Research 2014年第4期30卷 334-344页

作者： Luo Zhong-xuan Yu Ran Meng Zhao-liang School of Mathematical Sciences Dalian University of Technology School of Software Technology Dalian University of Technology

The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.

关键词： quadrature formula trigonometric function bi-orthogonality truncated complex moment problem

On Solving a System of Volterra Integral Equations with Relaxed Monte Carlo Method

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Journal of Applied Mathematics and Physics 2016年第7期4卷 1315-1320页

作者： Zhimin Hong Xiangzhong Fang Zaizai Yan Hui Hao Department of Mathematics Science College of Inner Mongolia University of Technology Hohhot China Department of Statistics School of Mathematical Sciences Peking University Beijing China

A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.

关键词： Systems of Volterra Integral Equations quadrature formula Relaxed Monte Carlo Method Importance Sampling

Quartic Spline interpolation on Uniform Meshes with Application to quadratures

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Journal of Mathematical Research with Applications 1999年第3期 533-538页

作者： A. A. Karaballi S. Sallam(Dept. of Math. and Comp Sci., Kuwait University, P.O.Box 5969, Safat, 13060 Kuwait)

1.IntroductionInterpolationbyquarticsplineshasbeeninvestigatedbyseveralauthors(of.[2],[3]).Itwasproved(see[4])thatgiventherealnumbers:{fi!}Zt’,{fi!+^}Z.’andfO,fN+1,whereAE[0,1],thenthereedestsau-niquequarticsplinese... 详细信息

关键词： interpolation quartic spline quadrature formula