In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysi...The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.展开更多
The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. Th...The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.展开更多
The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.
The ＂differential pattern＂ is an important thesis raised by Fei Xiaotong in his early sociology theory and possesses unique theoretical intension and practical value. From different dimensions, the study of the ＂di...The ＂differential pattern＂ is an important thesis raised by Fei Xiaotong in his early sociology theory and possesses unique theoretical intension and practical value. From different dimensions, the study of the ＂differential pattern＂ theory and its contemporary value has been one of the hot issues in domestic sociology. With these studies, the contents of the ＂differential pattern＂ theory are enriched, and also its value boundary and contemporary significance are revealed.展开更多
The mode characteristics for twin coupled microdisks are investigated by finite-difference time-domain technique. In the coupled microdisks,the same order whispering-gallery(WG) modes can form coupled modes with split...The mode characteristics for twin coupled microdisks are investigated by finite-difference time-domain technique. In the coupled microdisks,the same order whispering-gallery(WG) modes can form coupled modes with split mode wavelengths. We find that the coupled fundamental and first order WG modes can have anticrossing mode coupling as their wavelengths approach the same value in some case,which prevents the cross of the coupled mode wavelengths. The anticrossing mode coupling greatly reduces the coupled mode Q-factor,because the coupled mode field distribution transfers between the fundamental and the first order WG modes.展开更多
While participation in Social Network Sites （SNSs） has grown rapidly in recent years and is a highly popular and global phenomenon, only few research examined how the different cultural values and attitudes impact t...While participation in Social Network Sites （SNSs） has grown rapidly in recent years and is a highly popular and global phenomenon, only few research examined how the different cultural values and attitudes impact the way people adopt and use this new media platform. Employing qualitative approach, this study attempts to uncover the cross-cultural differences in motivations and behavioral patterns for using SNSs among the Korean and American users. The finding of this study shows the explicit differences in the motivations and strategies for using SNSs between Korean and American users, which is supported by the independent and interdependent self-construals theory proposed by Markus and Kitayama （1991）. The motivational themes and usage patterns emerged from Korean participants are more other- or relationship-focused, pursuing social/emotional support, while those of Americans are more ego- or self-focused, pertaining to entertainment or information seeking.展开更多
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establi...This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.展开更多
We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the ...We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition.展开更多
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...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.展开更多
文摘In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
基金supported by the"Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues"of the Chinese Academy of Sciences (Grant No.XDA01020304)
文摘The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.
基金Supported by the National Natural Science Foundation of China (40174003)
文摘The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.
文摘The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.
文摘The ＂differential pattern＂ is an important thesis raised by Fei Xiaotong in his early sociology theory and possesses unique theoretical intension and practical value. From different dimensions, the study of the ＂differential pattern＂ theory and its contemporary value has been one of the hot issues in domestic sociology. With these studies, the contents of the ＂differential pattern＂ theory are enriched, and also its value boundary and contemporary significance are revealed.
文摘The mode characteristics for twin coupled microdisks are investigated by finite-difference time-domain technique. In the coupled microdisks,the same order whispering-gallery(WG) modes can form coupled modes with split mode wavelengths. We find that the coupled fundamental and first order WG modes can have anticrossing mode coupling as their wavelengths approach the same value in some case,which prevents the cross of the coupled mode wavelengths. The anticrossing mode coupling greatly reduces the coupled mode Q-factor,because the coupled mode field distribution transfers between the fundamental and the first order WG modes.
文摘While participation in Social Network Sites （SNSs） has grown rapidly in recent years and is a highly popular and global phenomenon, only few research examined how the different cultural values and attitudes impact the way people adopt and use this new media platform. Employing qualitative approach, this study attempts to uncover the cross-cultural differences in motivations and behavioral patterns for using SNSs among the Korean and American users. The finding of this study shows the explicit differences in the motivations and strategies for using SNSs between Korean and American users, which is supported by the independent and interdependent self-construals theory proposed by Markus and Kitayama （1991）. The motivational themes and usage patterns emerged from Korean participants are more other- or relationship-focused, pursuing social/emotional support, while those of Americans are more ego- or self-focused, pertaining to entertainment or information seeking.
文摘This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
基金supported by National Natural Science Foundation of China(Grant Nos.11226330 and 11301343)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20113127120002)+3 种基金the Research Fund for Young Teachers Program in Shanghai(GrantNo.shsf018)the Fund for E-institute of Shanghai Universities(Grant No.E03004)supported by the Natural Sciences and Engineering Research Council of Canada(Grant No.OGP0046726)Shanghai University under Leading Academic Discipline Project of Shanghai MunicipalEducation Commission(Grant No.J50101)
文摘We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition.
文摘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.
