This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preservin...This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation.展开更多
This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstr...This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.展开更多
Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in detai...Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.展开更多
We introduce the definition of q-Stancu operator and investigate its approximation and shape-preserving property. With the help of the sign changes of f（x） and Ln = f（f, q;x） the shape-preserving property of q-Sta...We introduce the definition of q-Stancu operator and investigate its approximation and shape-preserving property. With the help of the sign changes of f（x） and Ln = f（f, q;x） the shape-preserving property of q-Stancu operator is obtained.展开更多
In the present paper, the shape-preserving properties and the monotonicity for convex functions of Stancu operator are given. Moreover, the simultaneous approximation problems of this operator are also considered.
In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ωξ-modulus of smoothness and preserve some natural kinds...In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ωξ-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].展开更多
Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem ...Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.展开更多
In this paper we apply a new method to choose suitable free parameters of the planar cubic G1 Hermite interpolant. The method provides the cubic G1 Hermite interpolant with minimal quadratic oscillation in average. We...In this paper we apply a new method to choose suitable free parameters of the planar cubic G1 Hermite interpolant. The method provides the cubic G1 Hermite interpolant with minimal quadratic oscillation in average. We can use the method to construct the optimal shape-preserving interpolant. Some numerical examples are presented to illustrate the effectiveness of the method.展开更多
A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are al...A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.展开更多
文摘This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation.
基金This work is supported by the Ntional Natural Science Foundation of China.
文摘This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.
基金Supported by the National Natural Science Foundation of China( 1 9971 0 1 7,1 0 1 2 5 1 0 2 )
文摘Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.
基金Supported by the Education Department of Zhejiang Province(20071078)
文摘We introduce the definition of q-Stancu operator and investigate its approximation and shape-preserving property. With the help of the sign changes of f（x） and Ln = f（f, q;x） the shape-preserving property of q-Stancu operator is obtained.
文摘In the present paper, the shape-preserving properties and the monotonicity for convex functions of Stancu operator are given. Moreover, the simultaneous approximation problems of this operator are also considered.
文摘In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ωξ-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].
基金Project supported by the National Natural Science Foundation of China(Nos.51378451 and 51378245)
文摘Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.
基金The Scientific Research Fund (18A415) of Hunan Provincial Education Department
文摘In this paper we apply a new method to choose suitable free parameters of the planar cubic G1 Hermite interpolant. The method provides the cubic G1 Hermite interpolant with minimal quadratic oscillation in average. We can use the method to construct the optimal shape-preserving interpolant. Some numerical examples are presented to illustrate the effectiveness of the method.
文摘A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.
