In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introduc...In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introducing new related variables and no matching is needed.The WKB approximation method problem can be solved.展开更多
We construct a positive type difference scheme for a singularly perturbed boundary value problem with a turning point. It's proved that this scheme is the second order convergence, uniformly in ? , to the solution...We construct a positive type difference scheme for a singularly perturbed boundary value problem with a turning point. It's proved that this scheme is the second order convergence, uniformly in ? , to the solution of the singularly perturbed B. V.P. Numerical examples are provided.展开更多
The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the...The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.展开更多
In this paper,we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method(PGFEM).We first give a priori estimate for the turning point problem with a single...In this paper,we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method(PGFEM).We first give a priori estimate for the turning point problem with a single boundary turning point.Then we use PGFEM to solve it,where test functions are the solutions to piecewise approximate dual problems.We prove that our method has a first-order convergence rate in both L∞h norm and a discrete energy norm when we select the exact solutions to dual problems as test functions.Numerical results show that our scheme is efficient for turning point problems with different types of singularities,and the convergency coincides with our theoretical results.展开更多
A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases abou...A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases about two small parameters. The asymptotic solutions to the problem are given. The structure of solutions and the different limit behaviors are revealed. And the solutions are compared with the exact solutions to the equation in which the coefficients are constants and a relatively more perfect result is obtained.展开更多
针对可见光图像弱小目标检测中的背景抑制和去噪问题,提出了奇异值分解(Singular Value Decomposition,SVD)带通滤波新方法.首先分析了图像奇异值与目标、噪声和图像背景的关系,结果表明奇异值的高序部分更多地反映图像噪声,中序部分更...针对可见光图像弱小目标检测中的背景抑制和去噪问题,提出了奇异值分解(Singular Value Decomposition,SVD)带通滤波新方法.首先分析了图像奇异值与目标、噪声和图像背景的关系,结果表明奇异值的高序部分更多地反映图像噪声,中序部分更多地反映目标性质,而低序部分更多地反映图像背景.以此为依据提出了SVD-Ⅰ型和SVD-Ⅱ型两种带通滤波器,并给出了奇异值曲线转折点法和门限准则法两种滤波器参数确定方法.实验表明SVD带通滤波能有效抑制图像背景,去除噪声,进而提高弱小目标的信噪比.展开更多
文摘In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introducing new related variables and no matching is needed.The WKB approximation method problem can be solved.
文摘We construct a positive type difference scheme for a singularly perturbed boundary value problem with a turning point. It's proved that this scheme is the second order convergence, uniformly in ? , to the solution of the singularly perturbed B. V.P. Numerical examples are provided.
文摘The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.
文摘In this paper,we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method(PGFEM).We first give a priori estimate for the turning point problem with a single boundary turning point.Then we use PGFEM to solve it,where test functions are the solutions to piecewise approximate dual problems.We prove that our method has a first-order convergence rate in both L∞h norm and a discrete energy norm when we select the exact solutions to dual problems as test functions.Numerical results show that our scheme is efficient for turning point problems with different types of singularities,and the convergency coincides with our theoretical results.
基金Supported by the National Natural Science Foundation of China(No.11071205)the Natural Foundation of Zhejiang Province (No.Y6110502)
文摘A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases about two small parameters. The asymptotic solutions to the problem are given. The structure of solutions and the different limit behaviors are revealed. And the solutions are compared with the exact solutions to the equation in which the coefficients are constants and a relatively more perfect result is obtained.
文摘针对可见光图像弱小目标检测中的背景抑制和去噪问题,提出了奇异值分解(Singular Value Decomposition,SVD)带通滤波新方法.首先分析了图像奇异值与目标、噪声和图像背景的关系,结果表明奇异值的高序部分更多地反映图像噪声,中序部分更多地反映目标性质,而低序部分更多地反映图像背景.以此为依据提出了SVD-Ⅰ型和SVD-Ⅱ型两种带通滤波器,并给出了奇异值曲线转折点法和门限准则法两种滤波器参数确定方法.实验表明SVD带通滤波能有效抑制图像背景,去除噪声,进而提高弱小目标的信噪比.
基金Supported by the National Natural Science Foundation of China(11202106)the Natural Science Foundation from the Education Bureau of Anhui Province(KJ2011A135)
