Sufficient conditions to guarantee the oscillations of fourth order ODE with impulses are obtained. The importance of the impulsive effect on the oscillations of higher order differential equations is stressed.
In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to...In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to a variety of boundary value problems in computational solid mechanics,such as eigenvalue problem,geometrical and material nonlinear problem,elastic contact problem and optimal design problems through some simple and representative examples,The advantage of such approach is that various ODE bounda- ry value problems in computational mechanics can be solved effectively in a unified manner by invoking a stand- ard ODE solver.展开更多
In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.展开更多
The existence of positive solutions is investigated for following semipositone nonlinear third-order three-point BVP ω''(t) - λf(t,w(t)) = 0, 0 ≤ t ≤ 1, ω(0) = ω'(n) = ω'(1) = 0.
Seasonal variation in surface ozone and the relationship between the background ozone concentration and wind were evaluated at Zhongshan Station,Antarctica using 2008 data.The wind frequency from the station area was ...Seasonal variation in surface ozone and the relationship between the background ozone concentration and wind were evaluated at Zhongshan Station,Antarctica using 2008 data.The wind frequency from the station area was only 2%,while the prevailing wind frequency was much larger (79.2%).This indicates that the surface ozone observations were not affected by the human activities at the station,and therefore could be counted as background concentrations of surface ozone along Antarctic coast.The concentration of surface ozone shows a distinct annual variation with the yearly mean of 25.0 nmol mol-1 and the maximum in winter,the minimum in summer.The surface ozone concentration had a strong negative correlation with ultraviolet radiation,and the mean values during polar night were one to two times higher than those in summer.These results imply that photochemical destruction of ozone dominates over Antarctica.The ozone depletion events at Zhongshan Station were obviously related to lower temperatures and higher BrO concentrations.Backward trajectory analysis reveals that the ozone depletion events are predominately caused by the high BrO concentrations.展开更多
In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required...In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.展开更多
By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact sol...By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV-sinh-Gordon equation by this approach.展开更多
The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. ...The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.展开更多
基金Project supported by Natural Science Foundation of Guangdong(011471)Natural Science Foundation of Guangdong Higher Education(0120).
文摘Sufficient conditions to guarantee the oscillations of fourth order ODE with impulses are obtained. The importance of the impulsive effect on the oscillations of higher order differential equations is stressed.
基金The project is supported by National Natural Science Foundation of China
文摘In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to a variety of boundary value problems in computational solid mechanics,such as eigenvalue problem,geometrical and material nonlinear problem,elastic contact problem and optimal design problems through some simple and representative examples,The advantage of such approach is that various ODE bounda- ry value problems in computational mechanics can be solved effectively in a unified manner by invoking a stand- ard ODE solver.
文摘In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
基金supported by the National Natural Science Foundation of China(41076132)the MOST Program of China(2006BAB18B05)
文摘Seasonal variation in surface ozone and the relationship between the background ozone concentration and wind were evaluated at Zhongshan Station,Antarctica using 2008 data.The wind frequency from the station area was only 2%,while the prevailing wind frequency was much larger (79.2%).This indicates that the surface ozone observations were not affected by the human activities at the station,and therefore could be counted as background concentrations of surface ozone along Antarctic coast.The concentration of surface ozone shows a distinct annual variation with the yearly mean of 25.0 nmol mol-1 and the maximum in winter,the minimum in summer.The surface ozone concentration had a strong negative correlation with ultraviolet radiation,and the mean values during polar night were one to two times higher than those in summer.These results imply that photochemical destruction of ozone dominates over Antarctica.The ozone depletion events at Zhongshan Station were obviously related to lower temperatures and higher BrO concentrations.Backward trajectory analysis reveals that the ozone depletion events are predominately caused by the high BrO concentrations.
基金Supported by the Natural Science Foundation of Hainan Province(80552)
文摘In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.
基金Project supported by the National Natural Science Foundation of China (Grant No 10672053)
文摘By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV-sinh-Gordon equation by this approach.
文摘The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.
