In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular different...In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular differential equations. Then we present the generalized Jacobi quasi-orthogonal approximation and its applica- tions to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions. We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains. Next, we consider the Hermite spectral method and the generalized Hermite spec- tral method with their applications. Finally, we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defined on unbounded domains. We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.展开更多
The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numeri...The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.展开更多
A Fourier pseudospectral-finite difference sheme is proposed for solving two-dimensionalvorticity equations. The generalized stability and the convergence are proved.The numericalresults are given.
In examining the historical changes in cognitive psychology from 1895 to 1949, it is necessary to transform cognitive psychology into cognitive practice. In the late Qing and early Republic era(1895-1919), cognitive p...In examining the historical changes in cognitive psychology from 1895 to 1949, it is necessary to transform cognitive psychology into cognitive practice. In the late Qing and early Republic era(1895-1919), cognitive practice mainly appeared as the cognition of the sick at heart. Against the background of the late Qing importation of Western learning aimed at securing national salvation, the intellectual class, represented by Tan Sitong,hastily dressed the wound to the traditional Chinese learning of Heaven and man inflicted by late nineteenth century scientific knowledge from Europe and America. They regarded cognition as the understanding gained in the practice of self-cultivation, as affording man a spiritual resting place between Heaven and Earth. By the time of the Republic of China(1920-1949), the main form of cognitive practice had become ghostly cognition.Under the banner of saving the country by means of science, higher education researchers,represented by Lu Zhiwei, explored cognition with the help of such intermediaries as physiological mechanisms and language structure. Men could easily become ghosts trapped in intermediaries when they plunged into the conceptual world in search of truth,as their cognitive practice evolved into the conceptual grasp of ghosts. This ghostly cognition continued into later information processing psychology and was disseminated among the mass of the public. A deeper level of the cognition of the sick at heart remains for future study, on the lengthy road home.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11171227)Fund for Doctoral Authority of China(Grant No.20123127110001)+1 种基金Fund for E-institute of Shanghai Universities(Grant No.E03004)Leading Academic Discipline Project of Shanghai Municipal Education Commission(Grant No.J50101)
文摘In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular differential equations. Then we present the generalized Jacobi quasi-orthogonal approximation and its applica- tions to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions. We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains. Next, we consider the Hermite spectral method and the generalized Hermite spec- tral method with their applications. Finally, we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defined on unbounded domains. We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.
文摘The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.
文摘A Fourier pseudospectral-finite difference sheme is proposed for solving two-dimensionalvorticity equations. The generalized stability and the convergence are proved.The numericalresults are given.
文摘In examining the historical changes in cognitive psychology from 1895 to 1949, it is necessary to transform cognitive psychology into cognitive practice. In the late Qing and early Republic era(1895-1919), cognitive practice mainly appeared as the cognition of the sick at heart. Against the background of the late Qing importation of Western learning aimed at securing national salvation, the intellectual class, represented by Tan Sitong,hastily dressed the wound to the traditional Chinese learning of Heaven and man inflicted by late nineteenth century scientific knowledge from Europe and America. They regarded cognition as the understanding gained in the practice of self-cultivation, as affording man a spiritual resting place between Heaven and Earth. By the time of the Republic of China(1920-1949), the main form of cognitive practice had become ghostly cognition.Under the banner of saving the country by means of science, higher education researchers,represented by Lu Zhiwei, explored cognition with the help of such intermediaries as physiological mechanisms and language structure. Men could easily become ghosts trapped in intermediaries when they plunged into the conceptual world in search of truth,as their cognitive practice evolved into the conceptual grasp of ghosts. This ghostly cognition continued into later information processing psychology and was disseminated among the mass of the public. A deeper level of the cognition of the sick at heart remains for future study, on the lengthy road home.
