In this paper, we shall study the initial boundary value problem of Schrodinger equation. The second order gradient superconvergence estimates for the problem are obtained solving by linear finite elements.
In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to...In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.展开更多
THE procedure of inertial confinement fusion (ICF) takes place in sub-nanosecond period. Inorder to investigate the hydrodynamic instability and asymmetry during the implosion, weneed to measure the two-dimensional di...THE procedure of inertial confinement fusion (ICF) takes place in sub-nanosecond period. Inorder to investigate the hydrodynamic instability and asymmetry during the implosion, weneed to measure the two-dimensional distribution of plasmas temperature and density as well asits relationship with time. For this purpose, an X-ray picosecond multiframe technique hasbeen developed.展开更多
文摘In this paper, we shall study the initial boundary value problem of Schrodinger equation. The second order gradient superconvergence estimates for the problem are obtained solving by linear finite elements.
文摘In the Stratonovich-Taylor and Stratonovich-Taylor-Hall discretization schemes for stochastic differential equations (SDEs), there appear two types of multiple stochastic integrals respectively. The present work is to approximate these multiple stochastic integrals by converting them into systems of simple SDEs and solving the systems by lower order numerical schemes. The reliability of this approach is clarified in theory and demonstrated in numerical examples. In consequence, the results are applied to the strong discretization of both continuous and jump SDEs.
文摘THE procedure of inertial confinement fusion (ICF) takes place in sub-nanosecond period. Inorder to investigate the hydrodynamic instability and asymmetry during the implosion, weneed to measure the two-dimensional distribution of plasmas temperature and density as well asits relationship with time. For this purpose, an X-ray picosecond multiframe technique hasbeen developed.
