Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 229-252, 2009, DOI:10.3970/cmc.2009.009.229

Abstract When the given input data are corrupted by an intensive noise, most numerical methods may fail to produce acceptable numerical solutions. Here, we propose a new numerical scheme for solving the Burgers equation forward in time and backward in time. A fictitious time τ is used to transform the dependent variable u(x,t) into a new one by (1+τ )u(x,t) =: v(x,t,τ), such that the original Burgers equation is written as a new parabolic type partial differential equation in the space of (x,t,τ). A fictitious damping coefficient can be used to strengthen the stability in the numerical integration of a semi-discretized… More >

Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang^2,3

CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 111-136, 2009, DOI:10.3970/cmc.2009.009.111

Abstract In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field C(x, t) at any time t< T. Then, we consider a direct regularization by adding an extra term αC(x,0) on the final condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution C^α(x,t) are provided and a… More >

Chein-ShanLiu¹

CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 219-234, 2009, DOI:10.3970/cmc.2009.013.219

Abstract The present paper reveals a new computational method for the illposed backward wave problem. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown initial data of velocity. Then, we consider a direct regularization to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain an analytical solution of regularization type. The sufficient condition of the data for the existence and uniqueness of solution is derived. The error estimate of the regularization solution is provided. Some numerical results illustrate the performance of the new method. More >

Yu Wang^1,2,*, Yan Cao², Liancheng Zhang², Hongtao Zhang³, Roxana Ohriniuc⁴, Guodong Wang⁵, Ruosi Cheng⁶

CMC-Computers, Materials & Continua, Vol.60, No.3, pp. 1171-1187, 2019, DOI:10.32604/cmc.2019.05575

Abstract Network traffic anomaly detection has gained considerable attention over the years in many areas of great importance. Traditional methods used for detecting anomalies produce quantitative results derived from multi-source information. This makes it difficult for administrators to comprehend and deal with the underlying situations. This study proposes another method to yet determine traffic anomaly (YATA), based on the cloud model. YATA adopts forward and backward cloud transformation algorithms to fuse the quantitative value of acquisitions into the qualitative concept of anomaly degree. This method achieves rapid and direct perspective of network traffic. Experimental results with standard dataset indicate that using… More >

Marin Marin¹, Ravi P. Agarwal², Mohamed Othman³

CMC-Computers, Materials & Continua, Vol.40, No.1, pp. 35-48, 2014, DOI:10.3970/cmc.2014.040.035

Abstract In this study we want to decide whether the decay of the solutions of the mixed initial boundary value problem in the context of thermoelasticiy of micropolar bodies with voids is sufficiently fast to guarantee that they vanish after a finite time. In fact, we prove that the effect of the micropolar structure in combination with the thermal and porous dissipation can not determine the thermomechanical deformations vanish after a finite time. More >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.24, No.3, pp. 209-238, 2011, DOI:10.3970/cmc.2011.024.209

Abstract In this study, we employ a semi-analytical scheme to resolve the three-dimensional backward heat conduction problem (BHCP) by utilizing a quasi-bound -ary concept. First, the Fourier series expansion method is used to estimate the temperature field u(x, y, z, t) at any time t < T. Second, we ponder a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for u(x, y, z, 0). The termwise separable property of the kernel function allows us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization parameter is recommended.… More >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.21, No.2, pp. 87-106, 2011, DOI:10.3970/cmc.2011.021.087

Abstract We address a new numerical approach to deal with these multi-dimensional backward wave problems (BWPs) in this study. A fictitious time τ is utilized to transform the dependent variable u(x, y, z, t) into a new one by (1+τ)u(x, y, z, t)=: v(x, y, z, t, τ), such that the original wave equation is written as a new hyperbolic type partial differential equation in the space of (x, y, z, t, τ). Besides, a fictitious viscous damping coefficient can be employed to strengthen the stability of numerical integration of the discretized equations by using a group preserving scheme. Several numerical… More >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.19, No.3, pp. 285-314, 2010, DOI:10.3970/cmc.2010.019.285

Abstract In this article, we propose a new numerical approach for solving these multi-dimensional nonlinear and nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time t is employed to transform the dependent variable u(x, y, z, t) into a new one by (1+t)u(x, y, z, t)=: v(x, y, z, t, t), such that the original nonlinear and nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, y, z, t, t). In addition, a fictitious viscous damping coefficient can be used to strengthen the stability of numerical integration of the discretized equations… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMC-Computers, Materials & Continua, Vol.19, No.1, pp. 17-36, 2010, DOI:10.3970/cmc.2010.019.017

Abstract The present study shows a backward group preserving scheme (BGPS) to deal with the multi-dimensional backward wave problem (BWP). The BWP is well-known as seriously ill-posed because the solution does not continuously count on the given data. When three numerical experiments are tested, we reveal that the BGPS is applicable to the multi-dimensional BWP. Even with noisy final data, the BGPS is also robust against perturbation. The numerical results are very pivotal in the computations of multi-dimensional BWP. More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 19-40, 2010, DOI:10.3970/cmc.2010.017.019

Abstract In this study, we employ a semi-analytical approach to solve a two-dimensional advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is used to calculate the concentration field C(x, y, t) at any time t < T. Then, we ponder a direct regularization by adding an extra termaC(x, y, 0) on the final time data C(x, y, T), to reach a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us obtaining a closed-form solution of the Fourier coefficients. A strategy to choose the regularization parameter is offered. The solver utilized in… More >