Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method

The Homotopy analysis method is applied to obtain the approximate solution of the Klein--Gordon--Schr?dinger equation. The Homotopy analysis solutions of the Klein--Gordon--Schr?dinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.     

Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the second-order backward differentiation formula for temporal discretization, the second-order Gear's extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.     

Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping

This paper concerns the convergence rate of solutions to a hyperbolic equation with $p(x)$-Laplacian operator and non-autonomous damping. We apply the Faedo-Galerkin method to establish the existence of global solutions, and then use some ideas from the study of second order dynamical system to get the strong convergence relationship between the global solutions and the steady solution. Some differential inequality arguments and a new Lyapunov functional are proved to show the explicit convergence rate of the trajectories.     

一类非线性发展方程的特征中心差分法

给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度u_t及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,u_t对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性.     

Estimation of the Reliability of a Stress–Strength System from Poisson Half Logistic Distribution

This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.     

一类大气浅水波方程的近似解

研究了一类非线性浅水波方程，利用同论映射理论和方法，得到了相应系统的近似解. 关键词： 浅水波 非线性 同伦映射 近似解     

基于微扰近似的圆锥表面光散射*

由Hueygen原理出发,介绍了粗糙表面的光散射特性.基于微扰近似,在不考虑遮蔽效应和圆锥顶点的散射情况下,分析了圆锥物体的光散射特性,推导了圆锥物体对平面光的散射场解析表达式.计算了圆锥表面在高度起伏均方根不同情况下对1.06μm光波的散射,并且得到了入射角一定的情况下,不同观察方向的散射光强分布曲线.结果表明,在观察方位角不变时,圆锥的散射光强随观察角顶角的增加先增大后减小|在观测方位角一定时,散射光强随高度起伏均方根的增加而减小,且随观察方位角呈对称分布.     

Approximate Homotopy Symmetry Reduction Method： Infinite Series Reductions to Kawahara Equation

The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered.     

Approximate Homotopy Symmetry Reduction Method: Infinite Series Reductions to Kawahara Equation

The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered.     

一类相对转动非线性动力学模型的近似解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动非线性动力学模型. 首先构造一个同伦映射, 其次决定方程的初始近似, 最后通过同伦映射方法得到了对应模型的任意次近似解. 关键词： 相对转动 非线性动力系统 近似解