Chih-Wen Chang¹, Jiang-Ren Chang¹, Chein-Shan Liu²

CMC-Computers, Materials & Continua, Vol.7, No.3, pp. 139-154, 2008, DOI:10.3970/cmc.2008.007.139

Abstract In this paper, we propose a Lie-group shooting method to deal with the classical Blasius flat-plate problem and to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf G(T) and the formation of a generalized mid-point Lie group element$\mathbf G(r). Then, by imposing G(T) = G(r) we can derive some algebraic equations to recover the missing initial conditions. It is the first time that we can apply the Lie-group shooting method to solve the classical Blasius flat-plate problem. Numerical examples are worked out to persuade that the novel approach has better… More >

Feng Guo¹, Pingzeng Liu^1,*, Wanming Ren², Ning Cao³, Chao Zhang¹, Fujiang Wen¹, Helen Min Zhou⁴

CMC-Computers, Materials & Continua, Vol.58, No.2, pp. 363-378, 2019, DOI:10.32604/cmc.2019.03794

Abstract In view of the problems such as frequent fluctuation of garlic price, lack of efficient forecasting means and difficulty in realizing the steady development of garlic industry, combined with the current situation of garlic industry and the collected data information. Taking Big Data platform of garlic industry chain as the core, using the methods of correlation analysis, smoothness test, co-integration test, and Granger causality test, this paper analyzes the correlation, dynamic, and causality between garlic price and young garlic shoot price. According to the current situation of garlic industry, the garlic industry service based on Big Data is put forward.… More >

Chein-Shan Liu^1,2, Chung-Lun Kuo³, Dongjie Liu⁴

CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 105-124, 2011, DOI:10.3970/cmc.2011.024.105

Abstract The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is very cheap. More >