共查询到20条相似文献,搜索用时 0 毫秒
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边界层型问题的插值摄动解法 总被引:3,自引:0,他引:3
本文在文[1]的基础上用插值摄动法研究了最高阶导数乘以小参数的二阶常微分方程的定解问题。算例表明,本文方法计算过程简单,其精度甚至比多重尺度法的一级近似结果的精度还稍高一些。 相似文献
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A perturbation method has been given for solving the Fredholmintegral equations of electrostatics as applied to tori of revolution,but under the restriction that there be in no case an appliedfield other than perhaps one that is uniform and parallel tothe axis of the torus. In the present paper this restrictionis removed, both for the conductor situation (Robin's equation)and the dielectric one (Durand's equation), and the generalizedmethod is illustrated by three applications. Two of these areto new problems which prove to be of considerable interest inthemselves, and one of the two leads to an example of significantfailure of the perturbation method. 相似文献
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Mohan K. Kadalbajoo Kailash C. Patidar 《Journal of Computational Analysis and Applications》2003,5(4):425-451
A numerical method based on cubic spline with adaptive grid is given for the self-adjoint singularly perturbed two point boundary value problems. The scheme derived in this method is second order accurate. Numerical examples are given to support the predicted theory. 相似文献
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Doklady Mathematics - A high-accuracy economical iterative method is proposed for calculating the potential and the strength of the electric field in a three-dimensional inhomogeneous spatially... 相似文献
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J. M. P. Booler 《The Journal of the Operational Research Society》1975,26(1):55-62
The method discussed provides an allocation of jobs to men in a transportation system. Each man is assigned a prespecified shift, associated with a base station, and returned to his base station at the end of his shift. The total number of men required is minimized, subject to a minimum time between jobs, a suitable lunch break, and the performance of all the jobs, employing the decomposition principle of linear programming. 相似文献
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《数学的实践与认识》2015,(21)
将同伦摄动法用于求解常微分方程四阶边值问题.通过将常微分方程边值问题转化为积分方程组,应用同伦摄动法求得近似解.给出同伦摄动法在两个具体的实例中的应用,并将近似解与精确解进行了比较,验证了同伦摄动法对求解线性、非线性常微分方程边值问题是一种非常有效的方法. 相似文献
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In this paper a general numerical method for solving Riemann problems is discussed. It can be used to solve the Riemann problems of various hyperbolic systems of differential equations with two independent variables. The problem of reflection of discontinuities from external boundaries can also be solved by this general numerical method. 相似文献
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A Discrete Lagrangian-Based Global-Search Method for Solving Satisfiability Problems 总被引:8,自引:0,他引:8
Satisfiability is a class of NP-complete problems that model a wide range of real-world applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method (DLM) for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, we show that an equilibrium is reached when a feasible assignment to the original problem is found and present heuristic algorithms to look for equilibrium points. Our method and analysis provides a theoretical foundation and generalization of local search schemes that optimize the objective alone and penalty-based schemes that optimize the constraints alone. In contrast to local search methods that restart from a new starting point when a search reaches a local trap, the Lagrange multipliers in DLM provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. In contrast to penalty-based schemes that rely only on the weights of violated constraints to escape from local minima, DLM also uses the value of an objective function (in this case the number of violated constraints) to provide further guidance. The dynamic shift in emphasis between the objective and the constraints, depending on their relative values, is the key of Lagrangian methods. One of the major advantages of DLM is that it has very few algorithmic parameters to be tuned by users. Besides the search procedure can be made deterministic and the results reproducible. We demonstrate our method by applying it to solve an extensive set of benchmark problems archived in DIMACS of Rutgers University. DLM often performs better than the best existing methods and can achieve an order-of-magnitude speed-up for some problems. 相似文献
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通过将互补问题转化为一种带非负约束的极小化问题 ,给出了求解互补问题的一种序列二次规划方法 .该方法中每一个子问题都是可解的 ,迭代产生的序列是非负的 ,在适当的条件下 ,分别证明了算法的全局收敛性、局部超线收敛性以及局部二次收敛性 . 相似文献
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D. Sun 《Applied Mathematics and Optimization》1999,40(3):315-339
In this paper we construct a regularization Newton method for solving the nonlinear complementarity problem (NCP(F )) and analyze its convergence properties under the assumption that F is a P
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-function. We prove that every accumulation point of the sequence of iterates is a solution of NCP(F ) and that the sequence of iterates is bounded if the solution set of NCP(F ) is nonempty and bounded. Moreover, if F is a monotone and Lipschitz continuous function, we prove that the sequence of iterates is bounded if and only if the solution
set of NCP(F ) is nonempty by setting , where is a parameter. If NCP(F) has a locally unique solution and satisfies a nonsingularity condition, then the convergence rate is superlinear (quadratic)
without strict complementarity conditions. At each step, we only solve a linear system of equations. Numerical results are
provided and further applications to other problems are discussed.
Accepted 25 March 1998 相似文献
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Monotone optimization problems are an important class of global optimization problems with various applications. In this paper,
we propose a new exact method for monotone optimization problems. The method is of branch-and-bound framework that combines
three basic strategies: partition, convexification and local search. The partition scheme is used to construct a union of
subboxes that covers the boundary of the feasible region. The convexification outer approximation is then applied to each
subbox to obtain an upper bound of the objective function on the subbox. The performance of the method can be further improved
by incorporating the method with local search procedure. Illustrative examples describe how the method works. Computational
results for small randomly generated problems are reported.
Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. The authors appreciate very much the discussions
with Professor Alex Rubinov and his suggestion of using local search. Research supported by the National Natural Science Foundation
of China under Grants 10571116 and 10261001, and Guangxi University Scientific Research Foundation (No. X051022). 相似文献
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It is well known that the gradient-projection algorithm plays an important role in solving minimization problems. In this paper, we will use the idea of regularization to establish a general method so that the sequence generated by the general method can be strongly convergent to a minimizer of constrained convex minimization problems, which solves a variational inequality under suitable conditions. 相似文献
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In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper. 相似文献