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A Multi-Domain Hybrid DG and WENO Method for Hyperbolic conservation laws.on Hybrid Meshes

Communications in Computational Physics 2014年第9期16卷 1116-1134页

作者： Jian Cheng Tiegang Liu LMIB School of Mathematics and Systems ScienceBeihang UniversityBeijing 100191P.R.China.

In[SIAM ***.,35(2)(2013),A1049–A1072],a class of multi-domain hybrid DG and WENO methods for conservation laws.was *** applications of this method showed that numerical instability may encounter if the DG flux with Lagrangian interpolation is applied as the interface flux during the moment of conservative *** this continuation paper,we present a more robust approach in the construction of DG flux at the coupling interface by using WENO procedures of *** on this approach,such numerical instability is overcome very *** addition,the procedure of coupling a DG method with a WENO-FD scheme on hybrid meshes is disclosed in *** testing cases are employed to demonstrate the accuracy of this approach and the stability underthe flexibility of using either WENO-FD flux or DG flux at the moment of requiring conservative coupling.

关键词： Discontinuous Galerkin method weighted essentially nonoscillatory scheme hybrid method conservation laws.

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HAMILTONIAN STRUCTURE AND INFINITE NUMBER OF conservation laws.FOR THE COUPLED DISCRETE KdV EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 2004年第4期19卷 374-380页

作者： YangHongxiang XuXixiang Dept.ofComput.Sci.andTech. TaishanCollegeTaian271021China. Dept.ofBasicCourses ShandongUniv.ofSci.andTech.Qingdao266510China.

A new discrete isospectral problem is introduced,from which the coupled discrete KdV hierarchy is deduced and is written in its Hamiltonian form by means of the trace *** is shown that each equation in the resulting h... 详细信息

关键词： discrete system Hamilton structure trace identity conservation laws.

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Combinations of nonstandard finite difference schemes and composition methods with complex time steps for population models

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International Journal of Biomathematics 2016年第4期9卷 1-14页

作者： Cuicui Liao Xiaohua Ding Jiuzhen Liang Department of Information and Computing Science Jiangnan University No. 1800 Lihu Avenue Wuxi Jiangsu 214122 P. R. China Department of Mathematics Harbin Institute of Technology at Weihai No. 2 Wenhua West Road Weihai Shandong 264209 P. R. China Department of Internet of ThingsJiangnan University No. 1800 Lihu Avenue Wuxi Jiangsu 214122 P. R. China

We propose an efficient numerical method for two population models, based on the nonstandard finite difference （NSFD） schemes and composition methods with complex time steps. The NSFD scheme is able to give positive numerical solutions that satisfy the conservation law, which is a key property for biological population models. The accuracy is improved by using the composition methods with complex time steps. Numerical tests on the plankton nutrient model and whooping cough model are presented to show the efficiency and advantage of the proposed numerical method.

关键词： Nonstandard finite difference schemes composition methods with complextime steps population models positive numerical solutions conservation laws.

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