This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. N...This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.展开更多
We solve the Laguerre-Gauss mode eigenvectors and eigenfunctions in the entangled state representation by searching for common eigenvectors of the 2-dimensional harmonic oscillator＇s total energy operator and the ang...We solve the Laguerre-Gauss mode eigenvectors and eigenfunctions in the entangled state representation by searching for common eigenvectors of the 2-dimensional harmonic oscillator＇s total energy operator and the angular momentum operator, We find that in the entangled state representation the eigen-solution satisfies the Hukuhara equation, and its solution is confluent hypergeometric function.展开更多
We propose a collocation method for solving initial value problems of secondorder ODEs by using modified Laguerre functions.This new process provides global numerical solutions.Numerical results demonstrate the effici...We propose a collocation method for solving initial value problems of secondorder ODEs by using modified Laguerre functions.This new process provides global numerical solutions.Numerical results demonstrate the efficiency of the proposed algorithm.展开更多
基金supported by the National Natural Science Foundation of China(No.11171227)the Ph.D.Programs Foundation of Ministry of Education of China(No.20080270001)+2 种基金the Shanghai Leading Academic Discipline Project(No.S30405)the Fund for E-Institute of Shanghai Universities(No.E03004)the Foundation for Distinguished Young Talents in Higher Education of Guangdong of China(No.LYM09138)
文摘This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.
基金The project supported by the President Foundation of the Chinese Academy of Sciences
文摘We solve the Laguerre-Gauss mode eigenvectors and eigenfunctions in the entangled state representation by searching for common eigenvectors of the 2-dimensional harmonic oscillator＇s total energy operator and the angular momentum operator, We find that in the entangled state representation the eigen-solution satisfies the Hukuhara equation, and its solution is confluent hypergeometric function.
基金supported in part by Foundation for Distinguished Young Talents in Higher Education of Guangdong,China,N.LYM09138supported in part by NSF of China N.10871131+2 种基金Fund for Doctor Authority of Chinese Educational Ministry N.20080270001Shanghai Leading Academic Discipline Project N.S30405Fund for E-institutes of Shanghai Universities N.E03004.
文摘We propose a collocation method for solving initial value problems of secondorder ODEs by using modified Laguerre functions.This new process provides global numerical solutions.Numerical results demonstrate the efficiency of the proposed algorithm.
