In this note, we apply numerical analysis to the first equation, find the conditions for it to have oscillating solutions and therefore solve an open problem posed by Peter A. Clarkson.
An operator-splitting algorithm for three-dimensional advection-diffusion-reaction equation is presented.The method of characteristics is adopted for the pure advection operator, the explicit difference scheme is used...An operator-splitting algorithm for three-dimensional advection-diffusion-reaction equation is presented.The method of characteristics is adopted for the pure advection operator, the explicit difference scheme is used for diffusion,and a prediction-correction scheme is em- ployed for reaction.The condition for stability of the algorithm is analysed.Severall inear and nonlinear examples are illustrated to test the convergence and accuracy of the numerical proce- dure,and satisfactory agreements between computed and analytical solutions are achieved.Due to its simplicity,stability,and validity for both one-and two-dimensional problems,the success- ful algorithm can be used to numerical simulations of viscous fluid flows,the transport of pollu- tants and sedimentations in reservoirs,lakes,rivers,estuaries and other environments,cooling- problems in heat or nuclear power plants,etc.展开更多
In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also ex...In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.展开更多
In this paper, we study a simplified model with delay for a control oftestosterone secretion. Employing the ejective fixed point principle due to Nussbaum, the existenceof slowly oscillating periodic solution of the m...In this paper, we study a simplified model with delay for a control oftestosterone secretion. Employing the ejective fixed point principle due to Nussbaum, the existenceof slowly oscillating periodic solution of the model is proven when the delay parameter r 】 r_0, forsome constant r_0 】 0.展开更多
基金the National Natural Science Foundation of China(No.60572073)School Foundation of Shandong University of Technology(No.304050)
文摘In this note, we apply numerical analysis to the first equation, find the conditions for it to have oscillating solutions and therefore solve an open problem posed by Peter A. Clarkson.
文摘An operator-splitting algorithm for three-dimensional advection-diffusion-reaction equation is presented.The method of characteristics is adopted for the pure advection operator, the explicit difference scheme is used for diffusion,and a prediction-correction scheme is em- ployed for reaction.The condition for stability of the algorithm is analysed.Severall inear and nonlinear examples are illustrated to test the convergence and accuracy of the numerical proce- dure,and satisfactory agreements between computed and analytical solutions are achieved.Due to its simplicity,stability,and validity for both one-and two-dimensional problems,the success- ful algorithm can be used to numerical simulations of viscous fluid flows,the transport of pollu- tants and sedimentations in reservoirs,lakes,rivers,estuaries and other environments,cooling- problems in heat or nuclear power plants,etc.
文摘In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.
基金Supported by the National Natural Science Foundation of China (No.19831030)The thesis is the production of the natural science research item for the 10th five-year plan in Jilin province office of education (No.200433).
文摘In this paper, we study a simplified model with delay for a control oftestosterone secretion. Employing the ejective fixed point principle due to Nussbaum, the existenceof slowly oscillating periodic solution of the model is proven when the delay parameter r 】 r_0, forsome constant r_0 】 0.
