Initial value methods for the primary two point boundary value problems in modeling viscoelastic flows

Initial value solvers through shooting methods will be used to compute solutions to the primary two-point boundary value problem arising in modeling viscoelastic flow. We will show that the classical Runge-Kutta methods will have at least h ²-order of convergence due to the presence of the singularity. Comparison with the work of others will also be presented through some numerical results and examples.     

两种半隐式三阶随机Runge-Kutta方法

根据彩色树理论,构造了两种求解Stratonovich型随机微分方程的半隐式三阶随机Runge-Kutta方法,给出了这两种方法的稳定性分析,其稳定区域比现有方法的稳定区域大;数值模拟的结果表明两个方法都具有较高的精度。     

时间最优开关控制的非线性规划方法

提出单输入非线性时间最优开关控制的非线性规划算法．针对不同的开关控制划分未知时间段，以时间段为变量建立与最优控制等价的非线性规划模型．构造每个未知时间段的等分龙格库塔格式，该格式不但不增加未知变量，而且可构造出不含导数的非线性规划算法．利用龙格库塔格式的收敛性和非线性规划的一阶最优性条件证明该方法的收敛性．最后以实例验证该算法．     

Note on filon-type integration for higher order exponential time differencing methods in stiff systems

The Filon-type quadrature is efficient for highly oscillatory functions — Fourier transforms. Based on Cox and Matthews’ ETD schemes, the higher order single step exponential time differencing schemes are presented based on the Filon-type integration and the A-stability of the two-order Adams-Bashforth exponential time differencing scheme is considered. The effectiveness and accuracy of the schemes is tested. Foundation item: Projects(02JJY2006, 03JJY2001) supported by Natural Science Foundation of Hunan Province; project supported by JSPS Fellowship Research Program     

一种改进的气动弹性时域推进方法

针对气动弹性控制方程,结构项采用标准龙格库塔方法推进,广义气动力项采用时间上的插值技术,发展了一种在每一时间步内只用计算一次非定常气动力的近似四阶龙格库塔推进方法。通过计算非线性Bernoulli方程和某一超音速翼面的气动弹性响应,证明该方法的时间准确度远高于采用气动力冻结技术的四阶龙格库塔方法。其准确度与标准龙格库塔方法相差不大,而其调用非定常气动力求解器的次数仅为其四分之一,大大提高了气动弹性数值模拟的效率。对于一般的气动弹性响应而言,该时间推进方法只用保证每个周期内的时间步在20～30个左右就能满足较高的准确度要求。     

Heat transfer enhancement in hydromagnetic dissipative flow past a moving wedge suspended by H2O-aluminum alloy nanoparticles in the presence of thermal radiation

This letter investigates the two dimensional magnetohydrodynamic Falkner Skan flow of water saturated with AA7072–H₂O and AA7075–H₂O nanoparticles over a moving wedge. Influence of viscous dissipation and thermal radiation is also under consideration. The model is reduced into nondimensional form by using defined self-similar transformations. Then, numerical study (Runge-Kutta numerical scheme) is carried out for solution purpose. The effects of pertinent flow parameters are discussed in the flow regimes by means of graphical aid. Graphical results for special cases (static wedge and when the movement of flow and wedge is in opposite direction) of the model are also elucidated graphically. It is noted that fluid velocity decreases for volumetric fraction and magnetic force favor the velocity. Significant effects of thermal radiation and nanoparticles volume fraction pointed for thermal filed and the influence of Eckert number is almost inconsequential. For more radiative fluid heat transfer coefficient decreases and nanoparticles volumetric fraction favor the local rate of heat transfer. In the presence of AA7075 nanoparticles, rate of heat transfer is quite rapid as compared to that of AA7072 nanoparticles. To validate the present computations, some present results are compared with already existing results in the literature and found better agreement between them. Finally, major points of the study ingrained in the last section of the letter.     

端面反射率对单端反射半导体光放大器的影响

本文考虑了光子密度、增益谱色散、放大自发辐射噪声(ASE)、端面反射率和载流子浓度对折射率的影响,并采用细化分段法及四阶龙格-库塔法求解速率方程及光场传输方程,分析了不同端面反射率时单端反射半导体光放大器(RSOA)的动态特性。结果表明端面反射率的适当增加,可以使增益得到提高,增益恢复时间减少, ASE输出功率增加,消光比下降。理论分析为优化RSOA的动态特性具有一定的指导意义。     

双掺杂LiNbO3晶体中光栅均匀性的优化研究

研究了非挥发全息记录中南于紫外光的强吸收而引起的光栅非均匀性，分析了这种非均匀性对光栅衍射效率的影响。结果显示，非均匀性致使光折变光栅的平均强度减弱，衍射效率降低。提出了采用两束等光强的敏化紫外光由晶体两侧入射的优化方案以改善光栅的均匀性，提高光栅的衍射效率。通过联立两中心带输运物质方程和双光束耦合波方程，进行了相应的理论模拟，并给出实验验证。结果表明双侧紫外光照射能够实现均匀性较好的光栅，是提高衍射效率的有效途径之一。     

Construction and implementation of general linear methods for ordinary differential equations: A review

It it the purpose of this paper to review the results on the construction and implementation of diagonally implicit multistage integration methods for ordinary differential equations. The systematic approach to the construction of these methods with Runge-Kutta stability is described. The estimation of local discretization error for both explicit and implicit methods is discussed. The other implementations issues such as the construction of continuous extensions, stepsize and order changing strategy, and solving the systems of nonlinear equations which arise in implicit schemes are also addressed. The performance of experimental codes based on these methods is briefly discussed and compared with codes from Matlab ordinary differential equation (ODE) suite. The recent work on general linear methods with inherent Runge-Kutta stability is also briefly discussed.     

战术弹道导弹再入段弹道仿真设计

在拦截TBM作战仿真系统中,需要模拟TBM再入段的弹道.文中在简化的大气模型下建立TBM的再入段方程,并采用龙格-库塔法来求解,通过仿真,可以看出模型符合仿真需要.