Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantit...Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.展开更多
This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that...This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.展开更多
基金Projects(50774026,50875059)supported by the National Natural Science Foundation of ChinaProject(20070420023)supported by the China Postdoctoral Science FoundationProject(2008AA03A239)supported by the High-tech Research and Development Program of China
基金Supported by the National Natural Science Foundation of China(1146103211401267+4 种基金11326238)the Natural Science Foundation of Jiangxi Province(20151bab201013)the Youth Foundation of Jiangxi Provincial Education Department(GJJ13376)the Research Foundation of Jiangxi University of Science and Techology(JxxJ bs1 2002nsfj 2015-K17)
文摘Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.
文摘This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.
