直线爆炸所形成的柱面波的近似分析解

由直线爆炸所形成的柱面波,文献[1]得到了数值解。本文对于绝热指数γ=C_p/C_v较大的情形,取ε=1/γ2为小参数,用伸缩坐标法得到了问题的一级近似分析解。算例(γ=3)表明,近似解与准确解(数值解)十分符合。     

用加权残余法求解含大参数的Duffing方程

本应用加权残余法分析了含大参数的Duffing方程,并得到了整个区域的（0＜ε＜∞）一致有效的近似解,得到的近似周期的最大相对误差小于7．0％,当参数为小量时（ε≤1）,得到的近似解和摄动解完全一致。     

可渗透壁面上Falkner-Skan磁流体动力学流动的近似解

研究了可渗透壁面上Falkner-Skan磁流体动力学（MHD）边界层流动问题．利用结合了微分变换法（DTM）和Padé近似的DTM-Padé方法,得到了边界层问题的近似解和壁摩擦因数值．通过建立一个迭代程序,边界层问题的近似解被表示为幂级数的形式,而且以图和表形式对不同参数下的近似解结果与打靶法得到的数值结果进行了对比,近似解和数值解结果高度吻合,从而验证了所得问题近似解和结论的可靠性和有效性．并且,对求得的边界层问题近似解结果进行了讨论,分析了不同物理参数对边界层流动的影响．     

一类球型区域上变系数反向热传导问题

考虑了一类球型区域上变系数反向热传导问题.这个问题是不适定的,即问题的解(若存在)并不连续依赖于测量数据.构造了投影迭代正则化方法,得到了该反问题的正则近似解,同时给出了在先验和后验参数选取规则下精确解与正则近似解之间的收敛性误差估计.最后,通过数值结果验证了该方法的有效性.     

两种块校正最小二乘问题的代数关系

1 引言 在求解工程问题中,我们常常应用最小二乘方法 min‖Ax-b‖_2,A∈R~(m×n),m≥n (1.1) x∈R~n去得到问题的数值近似解或估计系统的未知参数.我们常常已知(1)的解,而希望求解修改问题     

二维空间中半线性波动方程渐近理论的一个新结果

研究二维空间中一类半线性波动方程初值问题解的渐近理论 ,在 C2 (J× R2 ) (J ={ t|0≤ t≤ O(|ε|-1 2 -k(p-1 ) ) ,ε→ 0 ,0 <2 - k(p - 1 ) <1 ,0 相似文献   

非光滑向量均衡问题近似拟全局真有效解的最优性条件

本文研究一类非光滑向量均衡问题(Vector Equilibrium Problem)(VEP)关于近似拟全局真有效解的最优性条件.首先,利用凸集的拟相对内部型分离定理和Clarke次微分的性质,得到了问题(VEP)关于近似拟全局真有效解的最优性必要条件.其次,引入近似伪拟凸函数的概念,并给出具体实例验证其存在性,且在该凸性假设下建立了问题(VEP)关于近似拟全局真有效解的充分条件.最后,利用Tammer函数以及构建满足一定性质的非线性泛函,得到了问题(VEP)近似拟全局真有效解的标量化定理.     

一类广义非线性Schr(o)dinger扰动方程的泛函渐近解法

研究了一类非线性Schr(o)dinger扰动耦合系统.利用近似解相关联的特殊方法,首先讨论了对应的线性系统,并得到了其精确解.再利用泛函迭代的方法得到了非线性Schr(o)dinger扰动耦合系统的泛函渐近解析解.这个渐近解是一个解析式,还可对它进行解析运算.这对使用简单的模拟方法得到的近似解是达不到的.     

二维Helmholtz方程不适定问题的一种算子软化正则法

本文研究带有混合边界的二维Helmholtz方程不适定问题.为了获得稳定的数值解，利用基于de la ValléePoussin算子的软化正则方法，得到了正则近似解，给出正则近似解与精确解之间在先验参数选取规则之下的误差估计，并通过数值实验检验了数据有噪声扰动时方法的有效性和稳定性.     

多目标优化问题(ε,ε)-拟近似解的非线性标量化

本文研究了多目标优化问题的(ε,ε)-拟近似解.利用文献[1]给出的多目标优化问题统一的非线性标量化问题,在没有任何凸性条件下,研究了多目标优化问题的(ε,ε)-拟近似解的充分和必要条件.最后,利用文献[2]中给出的的范数,对多目标优化问题的(ε,ε)-拟近似解进行了非线性标量化刻画.本文第3节推广了文献[1]中的结果.     

On sensitive elliptic singular perturbation problems and logarithmic oscillations: the case of shells with edges

This work deals with singular perturbation problems depending on small positive parameter ?. The limit problem as ? → 0 has no solution within the classical theory of PDEs, which uses distribution theory. A very particular and less‐known phenomenon appears: large oscillations. These problems exhibit some kind of instability; very small and smooth variations of the data imply large singular perturbations of the solution. That kind of problems appears in elasticity for highly compressible two‐dimensional bodies and thin shells with elliptic middle surface with a part of the boundary free. Here, we consider certain properties of that oscillations and extend the theory to shells with edges. Copyright © 2012 John Wiley & Sons, Ltd.     

Falkner-Skan equation for flow past a stretching surface with suction or blowing: Analytical solutions

The simultaneous effects of suction and injection on tangential movement of a nonlinear power-law stretching surface governed by laminar boundary layer flow of a viscous and incompressible fluid beneath a non-uniform free with stream pressure gradient is considered. The self-similar flow is governed by Falkner-Skan equation, with transpiration parameter γ, wall slip velocity λ and stretching sheet (or pressure gradient) parameter β. The exact solution for β = −1 and three closed form asymptotic solutions for β large, large suction γ, and λ → 1 have also been presented. Dual solutions are found for β = −1 for each value of the transpiration parameter, including the non-permeable surface, for each prescribed value of the wall slip velocity λ. The large β asymptotic solution also dual with respect to wall slip velocity λ, but do not depend on suction and blowing. The critical values of γ, β and λ are obtained and their significance on the skin friction and velocity profiles is discussed. An approximate solution by integral method for a trial velocity profile is presented and results are compared with the exact solutions.     

A Newton Method for Linear Programming

A fast Newton method is proposed for solving linear programs with a very large (10⁶) number of constraints and a moderate (10²) number of variables. Such linear programs occur in data mining and machine learning. The proposed method is based on the apparently overlooked fact that the dual of an asymptotic exterior penalty formulation of a linear program provides an exact least 2-norm solution to the dual of the linear program for finite values of the penalty parameter but not for the primal linear program. Solving the dual problem for a finite value of the penalty parameter yields an exact least 2-norm solution to the dual, but not a primal solution unless the parameter approaches zero. However, the exact least 2-norm solution to the dual problem can be used to generate an accurate primal solution if mn and the primal solution is unique. Utilizing these facts, a fast globally convergent finitely terminating Newton method is proposed. A simple prototype of the method is given in eleven lines of MATLAB code. Encouraging computational results are presented such as the solution of a linear program with two million constraints that could not be solved by CPLEX 6.5 on the same machine.     

Numerics–characteristics–asymptotics: a case study from large scale ocean circulation

This paper uses a partial differential equation which occurs in a reduced model of large scale circulation in an ocean basin as an educational vehicle through which to demonstrate the usefulness of a set of mathematical techniques in analysing the equation. A parameter occurring in the equation does in reality vary from very small through intermediate to very large values. Therefore separate solutions are required for (a) very small, (b) very large and (c) intermediate values of the parameter. This allows for the demonstration of how when the parameter is very small the method of characteristics and the singular perturbation method are useful. When the parameter is very large the regular perturbation method is useful. At intermediate values of the parameter numerical methods must be used and in this case it is a helpful check to have available the asymptotic results for both small and large values of the parameter.     

An inexact implicit method for general mixed variational inequalities

In the present paper, we present an inexact implicit method with a variable parameter for general mixed variational inequalities. We use a self-adaptive technique to adjust parameter ρ$\rho$ at each iteration. The main advantage of this technique is that the method can adjust the parameter automatically and the numbers of iteration are not very sensitive to different initial parameter _ρ0.${\rho }_0.$     

Symmetry of two‐parameter homogeneous transition function

In this paper, we study a very interesting problem, that is, symmetry of the two parameters s,t>0 for a two‐parameter homogeneous transition function and obtain some important and interesting results.     

A least-squares preconditioner for radial basis functions collocation methods

Although meshless radial basis function (RBF) methods applied to partial differential equations (PDEs) are not only simple to implement and enjoy exponential convergence rates as compared to standard mesh-based schemes, the system of equations required to find the expansion coefficients are typically badly conditioned and expensive using the global Gaussian elimination (G-GE) method requiring flops. We present a simple preconditioning scheme that is based upon constructing least-squares approximate cardinal basis functions (ACBFs) from linear combinations of the RBF-PDE matrix elements. The ACBFs transforms a badly conditioned linear system into one that is very well conditioned, allowing us to solve for the expansion coefficients iteratively so we can reconstruct the unknown solution everywhere on the domain. Our preconditioner requires flops to set up, and storage locations where m is a user define parameter of order of 10. For the 2D MQ-RBF with the shape parameter , the number of iterations required for convergence is of order of 10 for large values of N, making this a very attractive approach computationally. As the shape parameter increases, our preconditioner will eventually be affected by the ill conditioning and round-off errors, and thus becomes less effective. We tested our preconditioners on increasingly larger c and N. A more stable construction scheme is available with a higher set up cost.     

Calculation of the Quality Parameter of Digital Nets and Application to Their Construction

In quasi-Monte Carlo methods, point sets of low discrepancy are crucial for accurate results. A class of point sets with low theoretic upper bounds of discrepancy are the digital point sets known as digital (t, m, s)-nets which can be implemented very efficiently. The parameter t is indicative of the quality; i.e., small values of t lead to small upper bounds of the discrepancy. We introduce an effective way to establish this quality parameter t for digital nets constructed over arbitrary finite fields and give an application to the construction of digital nets of high quality.     

A Large Sample Approximation to the Profile Plug-in Upper Confidence Limit

We consider the problem of constructing a 1– upper confidence limit for the scalar parameter ₀ in the presence of the nuisance parameter vector ₀, when the data are discrete. The 'profile plug-in' upper confidence limit is introduced by Kabaila and Lloyd. This confidence limit is based on computing a P-value from an estimator of ₀, replacing the nuisance parameter by the profile maximum likelihood estimate for known, and equating to . Theoretical and numerical evidence for the good coverage properties of this confidence limit is presented by Kabaila and Lloyd. An upper confidence limit should be assessed not only by its coverage properties but also by how large this confidence limit is. We measure how large the profile plug-in upper limit is by using a large sample approximation to it. This large sample approximation is used to delineate further the good properties of this confidence limit.     

Combining empirical likelihood and generalized method of moments estimators: Asymptotics and higher order bias

This paper proposes an estimator combining empirical likelihood (EL) and the generalized method of moments (GMM) by allowing the sample average moment vector to deviate from zero and the sample weights to deviate from n⁻¹. The new estimator may be adjusted through free parameter δ∈(0,1) with GMM behavior attained as δ?0 and EL as δ?1. When the sample size is small and the number of moment conditions is large, the parameter space under which the EL estimator is defined may be restricted at or near the population parameter value. The support of the parameter space for the new estimator may be adjusted through δ. The new estimator performs well in Monte Carlo simulations.