期刊文献+
共找到39篇文章
< 1 2 >
每页显示 20 50 100
ON TRUNCATION ERROR BOUND FOR MULTIDIMENSIONAL SAMPLING EXPANSION LAPLACE TRANSFORM 被引量:1
1
作者 LongJingfan 《Analysis in Theory and Applications》 2004年第1期52-57,共6页
The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for ... The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation. 展开更多
关键词 truncation error band limited function sampling theorem
下载PDF
An Optimal Spatial Finite-Difference Operator which ReducesTruncation Error to a Minimum
2
作者 王 元 伍荣生 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2002年第3期468-486,共19页
Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive err... Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique. Furthermore, the optimizing difference operator is consciously designed to be meshing-independent, so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or com-monly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro-posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly ex-cited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theo-retical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated. 展开更多
关键词 Finite—difference operator truncation error OPTIMIZATION
下载PDF
TRUNCATION ERROR REDUCTION METHOD FOR PLANAR CAVITY FLOW
3
作者 夏健 刘超群 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2001年第2期119-123,共5页
A new so called truncation error reduction method (TERM) is developed in this work. This is an iterative process which uses a coarse grid (2 h ) to estimate the truncation error and then reduces the error on the or... A new so called truncation error reduction method (TERM) is developed in this work. This is an iterative process which uses a coarse grid (2 h ) to estimate the truncation error and then reduces the error on the original grid ( h ). The purpose is to use coarse grids to get more accurate results and to develop a new method which could do coarse grid direct numerical simulation (DNS) for more accurate and acceptable DNS solutions. 展开更多
关键词 truncation error finite difference MULTIGRID
下载PDF
Double sampling derivatives and truncation error estimates
4
作者 Rashad M.Asharabi Aisha M.Al-Hayzea 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第2期209-224,共16页
This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the... This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself. This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula. 展开更多
关键词 double sampling series truncation error bounds convergence rate
下载PDF
Improved modal truncation error in the directly analytical method for damage identification of frame structures
5
作者 Yang Youfa Xu Dian +1 位作者 Huang Jing Liang Wenguang 《Engineering Sciences》 EI 2010年第4期91-96,共6页
The damage identification is made by the numerical simulation analysis of a five-storey-and-two-span RC frame structure, using improved and unimproved direct analytical method respectively; and the fundamental equatio... The damage identification is made by the numerical simulation analysis of a five-storey-and-two-span RC frame structure, using improved and unimproved direct analytical method respectively; and the fundamental equations were solved by the minimal least square method (viz. general inverse method). It demonstrates that the feasibility and the accuracy of the present approach were impoved significantly, compared with the result of unimproved damage identification. 展开更多
关键词 frame structures the directly analytical method damage identification the modal truncation error the minimal least square method
下载PDF
Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion 被引量:3
6
作者 YE Pei-xin SONG Zhan-jie 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第4期412-418,共7页
Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp(R) which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series ... Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp(R) which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ B^pΩ without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes L/(Wp(R)) are determined up to a logarithmic factor. 展开更多
关键词 Whittaker-Kotelnikov-Shannon theorem localized sampling truncation error aliasing error Sobolev class.
下载PDF
Uniform Truncation Error for Shannon Sampling Expansion from Local Averages 被引量:2
7
作者 Zhan-jie SONG Pei-xin YE +1 位作者 Ping WANG Shou-zhen ZENG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第1期121-130,共10页
Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p(R)which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averag... Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p(R)which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averages are obtained for functions f∈BpΩwith the decay condition f(t)≤A/t^δ,t≠0,where A and δare positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above. 展开更多
关键词 Shannon sampling Theorem local averages truncation error modulus of continuity
原文传递
Truncation Errors,Exact and Heuristic Stability Analysis of Two-Relaxation-Times Lattice Boltzmann Schemes for Anisotropic Advection-Diffusion Equation
8
作者 Irina Ginzburg 《Communications in Computational Physics》 SCIE 2012年第5期1439-1502,共64页
This paper establishes relations between the stability and the high-order truncated corrections for modeling of the mass conservation equation with the tworelaxation-times(TRT)collision operator.First we propose a sim... This paper establishes relations between the stability and the high-order truncated corrections for modeling of the mass conservation equation with the tworelaxation-times(TRT)collision operator.First we propose a simple method to derive the truncation errors from the exact,central-difference type,recurrence equations of the TRT scheme.They also supply its equivalent three-time-level discretization form.Two different relationships of the two relaxation rates nullify the third(advection)and fourth(pure diffusion)truncation errors,for any linear equilibrium and any velocity set.However,the two relaxation times alone cannot remove the leading-order advection-diffusion error,because of the intrinsic fourth-order numerical diffusion.The truncation analysis is carefully verified for the evolution of concentration waves with the anisotropic diffusion tensors.The anisotropic equilibrium functions are presented in a simple but general form,suitable for the minimal velocity sets and the d2Q9,d3Q13,d3Q15 and d3Q19 velocity sets.All anisotropic schemes are complemented by their exact necessary von Neumann stability conditions and equivalent finite-difference stencils.The sufficient stability conditions are proposed for the most stable(OTRT)family,which enables modeling at any Peclet numbers with the same velocity amplitude.The heuristic stability analysis of the fourth-order truncated corrections extends the optimal stability to larger relationships of the two relaxation rates,in agreementwith the exact(one-dimensional)and numerical(multi-dimensional)stability analysis.A special attention is put on the choice of the equilibrium weights.By combining accuracy and stability predictions,several strategies for selecting the relaxation and free-tunable equilibrium parameters are suggested and applied to the evolution of the Gaussian hill. 展开更多
关键词 Two-relaxation-times Lattice Boltzmann scheme AADE truncation errors von Neumann stability analysis numerical diffusion heuristic stability analysis
原文传递
EFFICIENT SIXTH ORDER P-STABLE METHODS WITH MINIMAL LOCAL TRUNCATION ERROR FOR y"=f(x,y)
9
作者 Kai-li Xiang R.M.Thomas 《Journal of Computational Mathematics》 SCIE CSCD 2002年第2期175-184,共10页
A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require on... A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require only three (new) function evaluation per iteration and per step integration. These methods have minimal local truncation error (LTE) and smaller phase-lag of sixth order than some sixth orders P-stable methods in [1-3,10-11]. The theoretical and numerical results show that these methods in this paper are more accurate and efficient than some methods proposed in [1-3,10]. 展开更多
关键词 second order periodic initial value problems P-stable PHASE-LAG local truncation error
全文增补中
Multivariate form of Hermite sampling series
10
作者 Rashad M.Asharabi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期253-265,共13页
In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sam... In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented. 展开更多
关键词 multidimensional sampling series sampling with partial derivatives contour integral truncation error
下载PDF
Error Analysis on Corrector Formula for Rectangular Rule 被引量:1
11
作者 XIAO Ze-chang DU Yue-peng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第2期270-275,共6页
This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound cor... This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis. 展开更多
关键词 numerical integration algebraic accuracy corrector formula truncation error convergence order
下载PDF
Improved Cotes Formula and Error Analysis 被引量:1
12
作者 DU Yue-peng XIAO Ze-chang 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期458-461,共4页
The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.
关键词 numerical integration algebraic accuracy truncation error convergence order
下载PDF
Stable Computer Method for Solving Initial Value Problems with Engineering Applications
13
作者 Mudassir Shams Nasreen Kausar +1 位作者 Ebru Ozbilge Alper Bulut 《Computer Systems Science & Engineering》 SCIE EI 2023年第6期2617-2633,共17页
Engineering and applied mathematics disciplines that involve differential equations in general,and initial value problems in particular,include classical mechanics,thermodynamics,electromagnetism,and the general theor... Engineering and applied mathematics disciplines that involve differential equations in general,and initial value problems in particular,include classical mechanics,thermodynamics,electromagnetism,and the general theory of relativity.A reliable,stable,efficient,and consistent numerical scheme is frequently required for modelling and simulation of a wide range of real-world problems using differential equations.In this study,the tangent slope is assumed to be the contra-harmonic mean,in which the arithmetic mean is used as a correction instead of Euler’s method to improve the efficiency of the improved Euler’s technique for solving ordinary differential equations with initial conditions.The stability,consistency,and efficiency of the system were evaluated,and the conclusions were supported by the presentation of numerical test applications in engineering.According to the stability analysis,the proposed method has a wider stability region than other well-known methods that are currently used in the literature for solving initial-value problems.To validate the rate convergence of the numerical technique,a few initial value problems of both scalar and vector valued types were examined.The proposed method,modified Euler explicit method,and other methods known in the literature have all been used to calculate the absolute maximum error,absolute error at the last grid point of the integration interval under consideration,and computational time in seconds to test the performance.The Lorentz system was used as an example to illustrate the validity of the solution provided by the newly developed method.The method is determined to be more reliable than the commonly existing methods with the same order of convergence,as mentioned in the literature for numerical calculations and visualization of the results produced by all the methods discussed,Mat Lab-R2011b has been used. 展开更多
关键词 Local truncation error CONSISTENCY computational time STABILITY lorentz system
下载PDF
Three Kinds of Discrete Formulae for the Caputo Fractional Derivative
14
作者 Zhengnan Dong Enyu Fan +1 位作者 Ao Shen Yuhao Su 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1446-1468,共23页
In this paper,three kinds of discrete formulae for the Caputo fractional derivative are studied,including the modified L1 discretisation forα∈(O,1),and L2 discretisation and L2C discretisation forα∈(1,2).The trunc... In this paper,three kinds of discrete formulae for the Caputo fractional derivative are studied,including the modified L1 discretisation forα∈(O,1),and L2 discretisation and L2C discretisation forα∈(1,2).The truncation error estimates and the properties of the coeffcients of all these discretisations are analysed in more detail.Finally,the theoretical analyses areverifiedby thenumerical examples. 展开更多
关键词 Caputo fractional derivative Modified L1 discretisation L2 discretisation L2C discretisation truncation error
下载PDF
On the Fractional Derivatives with an Exponential Kernel
15
作者 Enyu Fan Jingshu Wu Shaoying Zeng 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1655-1673,共19页
The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional d... The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional derivatives are proposed,including the Fourier transform and the Laplace transform.Then,the L2 discretisation for the exponential Caputo derivative with a∈(1,2)is established.The estimation of the truncation error and the properties of the coefficients are discussed.In addition,a numerical example is given to verify the correctness of the derived L2 discrete formula. 展开更多
关键词 Exponential fractional derivative Integral transform L2 discretisation truncation error
下载PDF
Storm surge simulation along the Meghna estuarine area:an alternative approach 被引量:2
16
作者 PAUL Gour Chandra SENTHILKUMAR Sukumar PRIA Rana 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2018年第1期40-49,共10页
In this study, numerical prediction of surges associated with a storm was made through the method of lines(MOL) in coordination with the newly proposed RKARMS(4, 4) method for the meghna estuarine region, along th... In this study, numerical prediction of surges associated with a storm was made through the method of lines(MOL) in coordination with the newly proposed RKARMS(4, 4) method for the meghna estuarine region, along the coast of Bangladesh. For this purpose, the vertically integrated shallow water equations(SWEs) in Cartesian coordinates were firstly transformed into ordinary differential equations(ODEs) of initial valued, which were then soloved using the new RKARMS(4, 4) method. Nested grid technique was employed for resolving the complexities of the region of interest with minimum cost. Fresh water discharge through the lower Meghna River was taken into account along the north east corner of the innermost child scheme. Numerical experiments were performed with the severe cyclone on April 1991 that crossed the coast over the study area. Simulated results by the study were found to be in good agreement with some reported data and were found to compare well with the results obtained by the MOL in addition with the classical 4th order Runge-Kutta(RK(4, 4)) method and the standard finite difference method(FDM). 展开更多
关键词 method of lines storm surge nested grid finite difference method RKARMS (4 4) method truncation errors
下载PDF
A New Method of Embedded Fourth Order with Four Stages to Study Raster CNN Simulation 被引量:2
17
作者 R. Ponalagusamy S. Senthilkumar 《International Journal of Automation and computing》 EI 2009年第3期285-294,共10页
A new Runge-Kutta (PK) fourth order with four stages embedded method with error control is presentea m this paper for raster simulation in cellular neural network (CNN) environment. Through versatile algorithm, si... A new Runge-Kutta (PK) fourth order with four stages embedded method with error control is presentea m this paper for raster simulation in cellular neural network (CNN) environment. Through versatile algorithm, single layer/raster CNN array is implemented by incorporating the proposed technique. Simulation results have been obtained, and comparison has also been carried out to show the efficiency of the proposed numerical integration algorithm. The analytic expressions for local truncation error and global truncation error are derived. It is seen that the RK-embedded root mean square outperforms the RK-embedded Heronian mean and RK-embedded harmonic mean. 展开更多
关键词 Raster scheme cellular neural network (CNN) numerical integration techniques edge detection new embedded RungeKutta root mean square (RKARMS (4 4)) method truncation errors.
下载PDF
A CLASS OF TWO-LEVEL EXPLICIT DIFFERENCE SCHEMES FOR SOLVING THREE DIMENSIONAL HEAT CONDUCTION EQUATION 被引量:1
18
作者 曾文平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第9期1071-1078,共8页
A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh rat... A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh ratio r = Deltat/(Deltax)(2) = Deltat/(Deltay)(2) = Deltat/(Deltaz)(2) less than or equal to 1/2, which is better than that of all the other explicit difference schemes. And when the order of truncation error is 0((Deltat)(2) + (Deltax)(4)), the stability condition is r less than or equal to 1/6, which contains the known results. 展开更多
关键词 three-dimensional heat conduction equation explicit difference scheme truncation error stability condition
下载PDF
A Class of High Accuracy Explicit Difference Schemes for Solving the Heat-conduction Equation of High-dimension 被引量:1
19
作者 CHEN Zhen-zhong MA Xiao-xia 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期236-243,共8页
In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O(τ^2+ h%4), and the stability c... In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O(τ^2+ h%4), and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis. 展开更多
关键词 heat-conduction equation explicit difference scheme truncation error conditional stability
下载PDF
A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations 被引量:2
20
作者 Yuxin Ren Yuxi Jiang +1 位作者 Miao'er Liu Hanxin Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第6期542-549,共8页
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We the... In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases. 展开更多
关键词 Incompressible Navier-Stokes equations Projection methods - Third-order scheme - Local truncation error
下载PDF
上一页 1 2 下一页 到第
使用帮助 返回顶部