Zhou YH^1,2, Wang XM², Wang JZ^1,2 , Liu XJ²

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.2, pp. 137-160, 2011, DOI:10.3970/cmes.2011.077.137

Abstract In this paper, we present an efficient wavelet-based algorithm for solving a class of fractional vibration, diffusion and wave equations with strong nonlinearities. For this purpose, we first suggest a wavelet approximation for a function defined on a bounded interval, in which expansion coefficients are just the function samplings at each nodal point. As the fractional differential equations containing strong nonlinear terms and singular integral kernels, we then use Laplace transform to convert them into the second type Voltera integral equations with non-singular kernels. Certain property of the integral kernel and the ability of explicit wavelet approximation to the nonlinear… More >

Caibin Zeng¹, Qigui Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 65-78, 2010, DOI:10.3970/cmes.2010.059.065

Abstract In this paper, a fractional order model is established to describe HIV internal viral dynamics involving HAART effect. First, the model is proved to possess non-negative solutions as desired in any population dynamics. Then, a detailed analysis is carried out to study the stability of equilibrium points. Numerical simulations are presented to illustrate the stability analysis. More >

Y. T. Gu¹, P. Zhuang², F. Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.3, pp. 303-334, 2010, DOI:10.3970/cmes.2010.056.303

Abstract Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation(FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions… More >

Chunhai Kou¹, Ye Yan², Jian Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 301-318, 2009, DOI:10.3970/cmes.2009.039.301

Abstract In the paper, stability for fractional order differential equations is studied. Then the result obtained is applied to analyse the stability of equilibrium for the model of HIV. More >