共查询到20条相似文献,搜索用时 15 毫秒
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In this paper we consider a modification of the Shishkin discretization mesh designed for the numerical solution of one-dimensional linear convection-diffusion singularly perturbed problems. The modification consists of a slightly different choice of the transition point between the fine and coarse parts of the mesh. This leads to a better layer-resolving mesh and to an improvement in the accuracy of the computed solution although the convergence order remains the same. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Fast solution of elliptic control problems 总被引:2,自引:0,他引:2
W. Hackbusch 《Journal of Optimization Theory and Applications》1980,31(4):565-581
Elliptic control problems with a quadratic cost functional require the solution of a system of two elliptic boundary-value problems. We propose a fast iterative process for the numerical solution of this problem. The method can be applied to very special problems (for example, Poisson equation for a rectangle) as well as to general equations (arbitrary dimensions, general region). Also, nonlinear problems can be treated. The work required is proportional to the work taken by the numerical solution of a single elliptic equation. 相似文献
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A. F. Izmailov A. L. Pogosyan 《Computational Mathematics and Mathematical Physics》2011,51(6):919-941
Mathematical programs with vanishing constraints are a difficult class of optimization problems with important applications
to optimal topology design problems of mechanical structures. Recently, they have attracted increasingly more attention of
experts. The basic difficulty in the analysis and numerical solution of such problems is that their constraints are usually
nonregular at the solution. In this paper, a new approach to the numerical solution of these problems is proposed. It is based
on their reduction to the so-called lifted mathematical programs with conventional equality and inequality constraints. Special
versions of the sequential quadratic programming method are proposed for solving lifted problems. Preliminary numerical results
indicate the competitiveness of this approach. 相似文献
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G. H. Meyer 《Numerische Mathematik》1970,16(3):248-267
A numerical method for the solution of the one-phase Stefan problem is discussed. By discretizing the time variable the Stefan problem is reduced to a sequence of free boundary value problems for ordinary differential equations which are solved by conversion to initial value problems. The numerical solution is shown to converge to the solution of the Stefan problem with decreasing time increments. Sample calculations indicate that the method is stable provided the proper algorithm is chosen for integrating the initial value problems. 相似文献
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Li-ping Wen Shou-fu Li 《计算数学(英文版)》2005,23(4):393-400
This paper is concerned with the stability of theoretical solution and numerical solutionof a class of nonlinear differential equations with piecewise delays.At first,a sufficientcondition for the stability of theoretical solution of these problems is given,then numericalstability and asymptotical stability are discussed for a class of multistep methods whenapplied to these problems. 相似文献
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V. I. Stashkevich 《Journal of Mathematical Sciences》1992,60(4):1568-1573
Matrix numerical differentiation algorithms are applied to construct numerical-analytical methods for approximate solution of boundary-value problems for the nonlinear one-dimensional equation of heat conduction. The problems are reduced to a system of differential equations for the values of the sought approximate solution in the interior grid nodes and also to numerical formulas for the solution values at the boundary nodes. A numerical experiment is conducted. The error relative to grid spacing is established.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 60, pp. 37–43, 1986. 相似文献
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C. Carthel R. Glowinski J. L. Lions 《Journal of Optimization Theory and Applications》1994,82(3):429-484
The present article is concerned with the numerical implementation of the Hilbert uniqueness method for solving exact and approximate boundary controllability problems for the heat equation. Using convex duality, we reduce the solution of the boundary control problems to the solution of identification problems for the initial data of an adjoint heat equation. To solve these identification problems, we use a combination of finite difference methods for the time discretization, finite element methods for the space discretization, and of conjugate gradient and operator splitting methods for the iterative solution of the discrete control problems. We apply then the above methodology to the solution of exact and approximate boundary controllability test problems in two space dimensions. The numerical results validate the methods discussed in this article and clearly show the computational advantage of using second-order accurate time discretization methods to approximate the control problems. 相似文献
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双曲-抛物型偏微分方程奇摄动混合问题的数值解法 总被引:1,自引:0,他引:1
石兰芳 《纯粹数学与应用数学》2003,19(2):106-111
构造了二阶双曲—抛物型方程奇摄动混合问题的差分格式,给出了差分解的能量不等式,并证明了差分解在离散范数下关于小参数一致收敛于摄动问题的解。 相似文献
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Hilbeth P. Azikri de Deus Claudio R. Ávila S. Jr. Ivan Moura Belo André T. Beck 《Applied Mathematical Modelling》2012
The numerical simulation of the mechanical behavior of industrial materials is widely used for viability verification, improvement and optimization of designs. Elastoplastic models have been used to forecast the mechanical behavior of different materials. The numerical solution of most elastoplastic models comes across problems of ill-condition matrices. A complete representation of the nonlinear behavior of such structures involves the nonlinear equilibrium path of the body and handling of singular (limit) points and/or bifurcation points. Several techniques to solve numerical problems associated to these points have been disposed in the specialized literature. Two examples are the load-controlled Newton–Raphson method and displacement controlled techniques. However, most of these methods fail due to convergence problems (ill-conditioning) in the neighborhood of limit points, specially when the structure presents snap-through or snap-back equilibrium paths. This study presents the main ideas and formalities of the Tikhonov regularization method and shows how this method can be used in the analysis of dynamic elastoplasticity problems. The study presents a rigorous mathematical demonstration of existence and uniqueness of the solution of well-posed dynamic elastoplasticity problems. The numerical solution of dynamic elastoplasticity problems using Tikhonov regularization is presented in this paper. The Galerkin method is used in this formulation. Effectiveness of Tikhonov’s approach in the regularization of the solution of elastoplasticity problems is demonstrated by means of some simple numerical examples. 相似文献
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A. G. Davydov E. V. Zakharov Yu. V. Pimenov 《Computational Mathematics and Modeling》2006,17(2):97-104
It is shown that hypersingular integral equations may be used for numerical solution of diffraction problems for electromagnetic
waves on magneto-dielectric bodies. The problem is reducible to surface equations with simple kernels, which permit applying
numerical schemes previously developed for ideally conducting objects. Examples of numerical solution of diffraction problems
on circular or square dielectric cylinders obtained from equations of different kinds are reported.
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Translated from Prikladnaya Matematika i Informatika, No. 20, pp. 5–15, 2005. 相似文献
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This article studies a numerical solution method for a special class of continuous time linear programming problems denoted
by (SP). We will present an efficient method for finding numerical solutions of (SP). The presented method is a discrete approximation algorithm, however, the main work of computing a numerical solution in
our method is only to solve finite linear programming problems by using recurrence relations. By our constructive manner,
we provide a computational procedure which would yield an error bound introduced by the numerical approximation. We also demonstrate
that the searched approximate solutions weakly converge to an optimal solution. Some numerical examples are given to illustrate
the provided procedure. 相似文献
13.
双曲-双曲奇异摄动混合问题的一致收敛格式 总被引:1,自引:0,他引:1
本文构造了二阶双曲-双曲奇异摄动混合问题的差分格式,给出了差分解的能量不等式,并证明了差分解在离散范数下关于小参数一致收敛于摄动问题的解. 相似文献
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The pricing of derivatives has gained considerable importance in the finance industry and leads to challenging problems in numerical optimization. We focus on the numerical solution of a stochastic model for option prices. In particular, we are concerned with the calibration of these models to real data, which leads to large scale optimization problems. We consider the numerical solution of these optimization problems and give some indication how to reduce the complexity of these problems. Special emphasis is devoted to a multi-layer strategy which is embedded into the optimization iteration. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A finite elernent methodology is developed for the numerical solution of traffic flow problems encountered in arterial streets. The simple continuum traffic flow model consisting of the equation of continuity and an equilibrium flow-density relationship is adopted. A Galerkin type finite element method is used to formulate the problem in discrete form and the solution is obtained by a step-by-step time integration in conjunction with the Newton-Raphson method. The proposed finite element methodology, which is of the shock capturing type, is applied to flow traffic problems. Two numerical examples illustrate the method and demonstrate its advantages over other analytical or numerical techniques. 相似文献
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Mohamed El-Gamel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,26(1):369-383
A numerical technique for solving time-dependent problems with variable coefficient governed by the heat, convection diffusion,
wave, beam and telegraph equations is presented. The Sinc–Galerkin method is applied to construct the numerical solution.
The method is tested on three problems and comparisons are made with the exact solutions. The numerical results demonstrate
the reliability and efficiency of using the Sinc–Galerkin method to solve such problems. 相似文献
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Abigail Wacher 《Central European Journal of Mathematics》2013,11(4):642-663
We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium equation, both in one dimension. Simulations are made for the two methods for: a) a travelling wave solution for the viscous Burgers’ equation, b) the Barenblatt selfsimilar analytical solution of the porous medium equation, and c) a waiting-time solution for the porous medium equation. Simulations are carried out for varying mesh sizes, and the numerical solutions are compared by computing errors in two ways. In the case of an analytic solution being available, the errors in the numerical solutions are computed directly from the analytic solution. In the case of no availability of an analytic solution, an approximation to the error is computed using a very fine mesh numerical solution as the reference solution. 相似文献
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Virginia Alarcón Sergio Amat Sonia Busquier David J. López 《Journal of Computational and Applied Mathematics》2008
In this paper, a modified Steffensen's type iterative scheme for the numerical solution of a system of nonlinear equations is studied. Two convergence theorems are presented. The numerical solution of boundary-value problems by the multiple shooting method using the proposed iterative scheme is analyzed. 相似文献