解一类二阶延迟常微分方程连续RKN方法的P-稳定性

In this paper, we study the P-stability of the continuous Runge-Kutta Nystroem method for solving the delayed second order differential equation that does not depend on y′. A general theorem is presented which can be used to obtain complete characterizations of the P-stability regions of these continuous RungeKutta- Nystroem methods. We use the condition to two given RKN methods.     

在优化工科数学教学质量系统中的几点做法与体会

介绍近二十年来对工科数学教学质量系统进行整体优化设计的几点做法与体会.     

Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients

In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.     

PERSISTENCE AND EXTINCTION OF A STOCHASTIC LOGISTIC MODEL WITH DELAYS AND IMPULSIVE PERTURBATION

A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.     

苏联时期高等工科数学教育:1970-1988

自1970年代初至苏联解体的近20年间,三次修订了数学教学大纲,不断加深了工科数学教育改革,提出了现代高等工科教育对数学教育的要求,建立了新的工科数学教育体系,对我国工科数学教育有重要参考价值.