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Dive into the research topics where Y. M. Cheng is active.

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Featured researches published by Y. M. Cheng.


Computers & Mathematics With Applications | 2014

The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation

L.W. Zhang; Y. J. Deng; K.M. Liew; Y. M. Cheng

Abstract A numerical study of two-dimensional Schrodinger equation is carried out using the improved complex variable element-free Galerkin (ICVEFG) method. The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrodinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. The stability and accuracy of the ICVEFG method are validated by comparing the computed results with the exact solutions.


International Journal of Computational Methods | 2013

AN INTERPOLATING BOUNDARY ELEMENT-FREE METHOD WITH NONSINGULAR WEIGHT FUNCTION FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

Jufeng Wang; Jianfei Wang; Fengxin Sun; Y. M. Cheng

In this paper, an improved interpolating moving least-squares (IIMLS) method with nonsingular weight function is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The IIMLS method can overcome the difficulties caused by the singularity of the weight function in the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas. By combining the boundary integral equation (BIE) method with the IIMLS method, an improved interpolating boundary element-free (IIBEF) method is presented for two-dimensional potential problems. The IIBEF method is a direct meshless boundary integral equation method in which the basic unknown quantities are the real solutions to the nodal variables, and the boundary conditions can be applied directly and easily. Thus, it gives greater computational precision. Some numerical examples are presented to demonstrate the IIMLS and IIBEF methods.


Applied Mathematics and Computation | 2014

Error estimates for the interpolating moving least-squares method

Jufeng Wang; Fengxin Sun; Y. M. Cheng; Aixiang Huang

In this paper, the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas is discussed in details. The advantage of the IMLS method is that the meshless method which is constructed based on the IMLS method can apply the essential boundary conditions directly and easily. A simpler expression of the approximation function of the IMLS method is obtained. Then the error estimate of the approximation function and its first and second order derivatives of the IMLS method are presented in one-dimensional case in this paper. The theoretical results show that if the order of the polynomial basis functions is big enough and the original function is sufficiently smooth, then the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper.


International Journal of Applied Mechanics | 2014

AN INTERPOLATING LOCAL PETROV–GALERKIN METHOD FOR POTENTIAL PROBLEMS

L. Chen; C. Liu; H. P. Ma; Y. M. Cheng

In this paper, based on the moving Kriging interpolation (MKI), the meshless interpolating local Petrov–Galerkin (ILPG) method is presented to solve two- and three-dimensional potential problems. In the present method, the shape function constructed by the MKI has the property of the Kronecker δ function. Then in the ILPG method the essential boundary conditions can be implemented directly. The discrete equations are obtained using the local symmetric weak form. The Heaviside step function is used as the test function in each sub-domain to avoid some domain integral in the symmetric weak form, which will greatly improve the effectiveness of the present method. The ILPG method in this paper is a truly meshless method, which does not require a mesh either for obtaining shape function or for numerical integration in the local weak form. Several numerical examples of potential problems show that the ILPG method has higher computational efficiency and convergence rate than the MLPG method.


International Journal of Applied Mechanics | 2016

An Improved Interpolating Element-free Galerkin Method for Elastoplasticity via Nonsingular Weight Functions

Fengxin Sun; Jufeng Wang; Y. M. Cheng

An improved interpolating element-free Galerkin (IIEFG) method for elastoplasticity is proposed in this paper. In the IIEFG method, the shape functions are constructed by the improved interpolating...


Applied Mathematics and Computation | 2013

A mathematical analysis of DNA damage induced G2 phase transition

L.W. Zhang; Y. M. Cheng; K.M. Liew

A mathematical model for DNA damage induced G2 phase transition is developed by integrating DNA damage signal pathway and G2 regulatory network. We have systematical identified the necessary parameters to be used in the mathematical analysis. Numerical studies are performed to investigate the dynamics of p53-Mdm2 feedback loop and evaluate the effect of DNA damage on G2 phase under various conditions. These studies are carried out to identify the important checkpoint and kinetic dynamics in G2 phase under the presence and absence of DNA damages. The predicted results are in consistent with biological findings. The mathematical model will be able to predict the dynamic behaviors of cellular networks in response to DNA damage in G2 phase under different damage conditions.


Applied Mathematics and Computation | 2014

Mathematical modeling of p53 pulses in G2 phase with DNA damage

L.W. Zhang; Y. M. Cheng; K.M. Liew

Abstract A mathematical model of p53 pulses involved in G2/M phase transition is proposed to study the response of p53-centered signaling network and checkpoint mechanisms of G2 phase to DNA damages. The oscillation by p53-Mdm2 feedback loop as the response to DNA damage is first simulated. This follows by modeling the signaling network in G2 phase and realizing its importance in cell cycle progression. The signaling network is used to assess effects of different intensities of DNA damage on G2 phase transition. An examination of the dynamics of cell fate decision module shows that p53 arrester and Wip1 play key roles in DNA repair and may be an important target of cancer therapy. The present numerical analysis based on the proposed model may be useful for the inference of p53-mediated mechanisms in response to DNA damage in G2 phase under different damage conditions.


Applied Mathematics and Computation | 2014

A mathematical study of the robustness of G2/M regulatory network in response to DNA damage with parameters sensitivity

L.W. Zhang; Y. M. Cheng; K.M. Liew

Abstract A mathematical analysis of G2/M regulatory network is carried out by performing a study of the robustness of biological systems with kinetic parameters sensitivity. Numerical experiments are performed to investigate local sensitivity to identified significant kinetic parameters relevant to key proteins involved in G2/M phase transition. A global sensitivity analysis is performed to reveal the relationship between the probability of a DNA-damaged cell passing through as a healthy cell and the initial perturbation of parameters in the G2/M model. Using statistical hypothesis testing with the Type II error, this enables prediction of robustness of cell cycle to DNA damage signal when the global perturbation of G2/M regulatory network is small enough. It is found that the robustness of G2/M network declines as the level of the DNA damage rises. The aforementioned findings are inconsistent with existing experimental observations.


Computational Mechanics | 2005

Numerical manifold method based on the method of weighted residuals

S. Li; Y. M. Cheng; Y.-F. Wu


Computational Mechanics | 2015

The complex variable reproducing kernel particle method for the analysis of Kirchhoff plates

L. Chen; Y. M. Cheng; Hang Ma

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K.M. Liew

City University of Hong Kong

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Fengxin Sun

Ningbo University of Technology

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L.W. Zhang

Shanghai Jiao Tong University

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Aixiang Huang

Xi'an Jiaotong University

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S. Li

Shanghai University

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D.M. Li

City University of Hong Kong

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Y. J. Deng

City University of Hong Kong

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Y.-F. Wu

City University of Hong Kong

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