Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the...Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the scheme through its modified equations andshows that the first order Lax-Friedrichs scheme to approach BV solutions of the convectionequation has L￣2-error bounds of O(△x￣(1/4)),where △x is the discrete mesh length.Nemericalexperiments are presented and numerical results justify the theoretical analysis.展开更多
Equilibrium moisture content （EMC） data for rough rice of thirteen Chinese varieties were obtained by static gravimetric method at five different temperatures （10, 20, 25, 30, and 35 ℃） and 11% to 96% equilibrium...Equilibrium moisture content （EMC） data for rough rice of thirteen Chinese varieties were obtained by static gravimetric method at five different temperatures （10, 20, 25, 30, and 35 ℃） and 11% to 96% equilibrium relative humidity （ERH）. Six models, i.e., Brunauer-Emmett-Teller, Guggenheim-Anderson-deBoer, Modified Chung-Pfost （MCPE）, Modified Henderson, Modified Oswin, and Strohman-Yoerger （STYE） fitted the EMC/ERH data based on the coefficient of determination, residue sum-of-squares, standard error of estimate, and mean relative percent error. The best fitted equations were MCPE and STYE, but MCPE is three-parameter, readily transformed equation and adopted in this study. The isosteric heats for both rough rice desorption and adsorption, and for both the sorption of Japonica and Indica rice, decreased rapidly with an increase in seed moisture content （m.c.） until the m.c. of 20% dry basis （d.b.） reached, and thereafter they decreased smoothly with increasing moisture content. The isosteric heats of rough rice desorption were higher than those of adsorption below the m.c. of 22.5% d.b., but thereafter, there was no significant difference found between desorption and adsorption. The sorption isosteric heats of Indica rice were slightly higher than those of Japonica rice under all moisture contents at a constant temperature. These results provide a sound basis for future work on the drying and storage of rice.展开更多
The error equation of a rotating inertial navigation system was introduced. The effect of the system's main error source (constant drift of gyro and zero bias of accelerometer) under rotating conditions for the sy...The error equation of a rotating inertial navigation system was introduced. The effect of the system's main error source (constant drift of gyro and zero bias of accelerometer) under rotating conditions for the system was analyzed. Validity of theoretical analysis was shown via simulation, and that provides a theoretical foundation for a rotating strap-down inertial navigation system during actual experimentation and application.展开更多
In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability c...In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.展开更多
In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2...In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2)-norm is obtained.展开更多
The ability to predict groundwater fluxes with a minimum of effort and measurement is an important objective. Numerical modeling is one approach to obtain such a prediction. Predictions of groundwater fluxes can be us...The ability to predict groundwater fluxes with a minimum of effort and measurement is an important objective. Numerical modeling is one approach to obtain such a prediction. Predictions of groundwater fluxes can be used to determine fluxes of other materials such as salt and nutrients. In this paper an analytical model is developed to predict the flow of groundwater from mangrove forest to the creek. The model uses the geometry and hydraulic conductivity of the mangrove forest sediment, which is inundated by tidal water from day zero to day five, with the flux ranged from 0.026 to 0.007 m^3/（m^2.day） with the average error is about 10%. The solution for the groundwater flow is written in terms of an analytic series solution, based on two dimensional potential flow. The approach is basically to solve the hydraulic potential flow for steady state conditions using the Laplace equation. The advantages of this method are that it is simple but accurate, and the error in the computation can be readily calculated. The result of this model is then compared to the result of the field measurement from also day zero to day five after inundation, which ranged from 0.030 to 0.013 m3/（m2.day） with the average error is about 40%. From the above results, it is concluded that the series solution model can be used to calculate the flux of the groundwater, especially in the mangrove forest area.展开更多
The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0...The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.展开更多
The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundar...The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.展开更多
A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis i...A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.展开更多
文摘Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the scheme through its modified equations andshows that the first order Lax-Friedrichs scheme to approach BV solutions of the convectionequation has L￣2-error bounds of O(△x￣(1/4)),where △x is the discrete mesh length.Nemericalexperiments are presented and numerical results justify the theoretical analysis.
文摘Equilibrium moisture content （EMC） data for rough rice of thirteen Chinese varieties were obtained by static gravimetric method at five different temperatures （10, 20, 25, 30, and 35 ℃） and 11% to 96% equilibrium relative humidity （ERH）. Six models, i.e., Brunauer-Emmett-Teller, Guggenheim-Anderson-deBoer, Modified Chung-Pfost （MCPE）, Modified Henderson, Modified Oswin, and Strohman-Yoerger （STYE） fitted the EMC/ERH data based on the coefficient of determination, residue sum-of-squares, standard error of estimate, and mean relative percent error. The best fitted equations were MCPE and STYE, but MCPE is three-parameter, readily transformed equation and adopted in this study. The isosteric heats for both rough rice desorption and adsorption, and for both the sorption of Japonica and Indica rice, decreased rapidly with an increase in seed moisture content （m.c.） until the m.c. of 20% dry basis （d.b.） reached, and thereafter they decreased smoothly with increasing moisture content. The isosteric heats of rough rice desorption were higher than those of adsorption below the m.c. of 22.5% d.b., but thereafter, there was no significant difference found between desorption and adsorption. The sorption isosteric heats of Indica rice were slightly higher than those of Japonica rice under all moisture contents at a constant temperature. These results provide a sound basis for future work on the drying and storage of rice.
基金the Nature Science Foundation of China under Grant No.60604019 and No.6075001
文摘The error equation of a rotating inertial navigation system was introduced. The effect of the system's main error source (constant drift of gyro and zero bias of accelerometer) under rotating conditions for the system was analyzed. Validity of theoretical analysis was shown via simulation, and that provides a theoretical foundation for a rotating strap-down inertial navigation system during actual experimentation and application.
基金Supported by NSF of the Education Department of Henan Province(20031100010)
文摘In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.
基金supported by NSF of China(60874039)Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50101)
文摘In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2)-norm is obtained.
文摘The ability to predict groundwater fluxes with a minimum of effort and measurement is an important objective. Numerical modeling is one approach to obtain such a prediction. Predictions of groundwater fluxes can be used to determine fluxes of other materials such as salt and nutrients. In this paper an analytical model is developed to predict the flow of groundwater from mangrove forest to the creek. The model uses the geometry and hydraulic conductivity of the mangrove forest sediment, which is inundated by tidal water from day zero to day five, with the flux ranged from 0.026 to 0.007 m^3/（m^2.day） with the average error is about 10%. The solution for the groundwater flow is written in terms of an analytic series solution, based on two dimensional potential flow. The approach is basically to solve the hydraulic potential flow for steady state conditions using the Laplace equation. The advantages of this method are that it is simple but accurate, and the error in the computation can be readily calculated. The result of this model is then compared to the result of the field measurement from also day zero to day five after inundation, which ranged from 0.030 to 0.013 m3/（m2.day） with the average error is about 40%. From the above results, it is concluded that the series solution model can be used to calculate the flux of the groundwater, especially in the mangrove forest area.
文摘The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.
基金supported by National National Science Foundation of China(Grant No.10971116)FRG of Hong Kong Baptist University(Grant No.FRG1/11-12/051)
文摘The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10671184 and 10971203.
文摘A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.
