In this paper, spectral and pseudospectral methods are applied to both time and space variables for parabolic equations. Spectral and pseudospectral schemes are given, and error estimates are obtained for approximate ...In this paper, spectral and pseudospectral methods are applied to both time and space variables for parabolic equations. Spectral and pseudospectral schemes are given, and error estimates are obtained for approximate solutions.展开更多
This paper presents a fully spectral discretization method for solving KdV equations with periodic boundary conditions.Chebyshev pseudospectral approximation in the time direction and Fourier Galerkin approximation in...This paper presents a fully spectral discretization method for solving KdV equations with periodic boundary conditions.Chebyshev pseudospectral approximation in the time direction and Fourier Galerkin approximation in the spatial direction.The expansion coefficients are determined by minimizing an object funictional.Rapid convergence of the method is proved.展开更多
The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant...The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant( LTI) system and a static nonlinear function( the linear part is followed by the nonlinear part). The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output( MISO) linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.展开更多
For solving Burgers' equation with periodic boundary conditions, this paper preseats a fully spectral discretisation method: Fourier Galerkin approximation in the spatial direction and Chebyshev pseudospectral app...For solving Burgers' equation with periodic boundary conditions, this paper preseats a fully spectral discretisation method: Fourier Galerkin approximation in the spatial direction and Chebyshev pseudospectral approximation in the time direction. The expansion coefficients are determined by means of minimizing an object functional, and rapid convergence of the method is proved.展开更多
文摘In this paper, spectral and pseudospectral methods are applied to both time and space variables for parabolic equations. Spectral and pseudospectral schemes are given, and error estimates are obtained for approximate solutions.
文摘This paper presents a fully spectral discretization method for solving KdV equations with periodic boundary conditions.Chebyshev pseudospectral approximation in the time direction and Fourier Galerkin approximation in the spatial direction.The expansion coefficients are determined by minimizing an object funictional.Rapid convergence of the method is proved.
文摘The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant( LTI) system and a static nonlinear function( the linear part is followed by the nonlinear part). The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output( MISO) linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.
文摘For solving Burgers' equation with periodic boundary conditions, this paper preseats a fully spectral discretisation method: Fourier Galerkin approximation in the spatial direction and Chebyshev pseudospectral approximation in the time direction. The expansion coefficients are determined by means of minimizing an object functional, and rapid convergence of the method is proved.
