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1.
A shooting method for coupled Prfer equations is discussedfor numerical solution of two-parameter Sturm-Liouville problems.
Research supported in part by grants from the NSERC of Canada. 相似文献
2.
Bai Xiaoming; Yang Xiao-Song; Li Huimin 《IMA Journal of Mathematical Control and Information》2007,24(4):483-491
3.
Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws 总被引:4,自引:0,他引:4
The theory of optimal recovery is applied to finite volume methodsfor the numerical solution of conservation laws in multiplespace dimensions. Classical polynomial EN0 (essentially non-oscillatory)algorithms can be interpreted as trivial recovery operatorsfor the point functional in the light of this theory. Thin platesplines are identified as optimal recovery functions in Beppo-Levispaces and can be seen as multi-dimensional analogues of cubicsplines. Recovery algorithms of ENO-type based on thin platesplines are developed and applied to test problems includingthe Euler equations of compressible gas dynamics.
E-mail: Thomas.Sonar{at}ts.go.dlr.de 相似文献
4.
Perturbations of the equation are discussed. The structure of near-orthogonal matrices is shown, and implicationsfor certain control problems are pointed out. Examples are givenand the circumstances are noted in which the real part of aneigenvalue can be expected to change sign.
This paper was written while the author was on a Leave of Absenceat the Department of Mathematics, University of Salford. 相似文献
5.
A concise review is given of some recent methods for performingalgebraic operations on polynominal matrices. The problems addressedare division, inversion, and extraction of greatest common divisorof a pair of matrices.
Based on a presentation at the International Symposium on theMathematical theory of Networks and Systems, Amsterdam, June1989. 相似文献
6.
In this paper we consider a monotonic and conservative variationon the direct Lagrange-Galerkin method due to Priestley, andaddress certain problems with both the original Lagrange-Galerkinmethod and this new method which disappear with the use of higher-orderC1 basis functions. Here we concentrate on the use of Hermite-cubics,demonstrating their superior stability in the Lagrange- Galerkinmethod, and the adaptations of the recovery techniques neededto ensure monotonicity and near conservation.
Current address: Schlumberger GeoQuest, Abingdon Business Park,Oxon OX14 10 UK. 相似文献
7.
The Method of Fundamental Solutions for the Solution of Nonlinear Plane Potential Problems 总被引:2,自引:0,他引:2
The method of fundamental solutions is described for the solutionof elliptic boundary value problems governed by Laplace's equationin the plane subject to nonlinear radiation-type boundary conditions.The effectiveness of the method is demonstrated by examiningits performance on two problems from the literature, and comparisonsare made with published results obtained using boundary elementmethods.
Portions of this work were conducted while this author wasa visiting assistant professor at the University of Kentucky.
Partially supported by the National Science Foundation undergrant MCS-8303287 and grant RII-8610671, and by the Commonwealthof Kentucky through the Kentucky EPSCoR Program. 相似文献
8.
We consider singularly perturbed high-order elliptic two-pointboundary value problems of reaction-diffusion type. It is shownthat, on an equidistant mesh, polynomial schemes cannot achievea high order of convergence that is uniform in the perturbationparameter. Piecewise polynomial Galerkin finite-element methodsare then constructed on a Shishkin mesh. Almost optimal convergenceresults, which are uniform in the perturbation parameter, areobtained in various norms. Numerical results are presented fora fourth-order problem.
e-mail address: stynes{at}bureau.ucc.ie. 相似文献
9.
This paper discusses the construction of an approximate solutionto the standard fast-slow system of equations. The usual representationin terms of a fast vector and a slow vector is shown to be satisfactoryonly when certain matrices are neither ill conditioned nor near-orthogonal.Applications of the results to certain control problems areinvestigated.
This paper was written while on Leave of Absence at the Departmentof Mathematics, University of Salford, Salford. 相似文献
10.
For the system representing a chain of coupled vibrating strings,we show that the associated semigroup satisfies the assumptionof spectrum-determined growth, and hence obtain conditions forenergy to decay strongly or exponentially. We examine in detailthe three-string case, and our results include those obtainedby others for the two-string case.
Permanent address: Beijing Institute of Information and Control,Beijing, China. 相似文献
11.
Kuera's completely algebraic method is used to derive a polynomialsolution with only one Diophantine equation for least-squaresdeterministic control in discrete-time. The same method is used,again involving only one Diophantine equation, to derive themultivariable discrete-time Wiener filter.
This paper was presented at the IMA Symposium on Control Theory,Somerville College,Oxford, September 1986. 相似文献
12.
The aim of the present paper is to study the stability propertiesof the numerical methods for pure delay differential equations.The methods we consider are based on a quadrature rule and aninterpolant (NCE) to get an approximation of the retarded part(continuous quadrature rule). As a test equation we consider
and we give sufficient conditions for the boundedness of thesolutions. The same behaviour is preserved by the continuousquadrature rule under some restriction on the parameters. Asa conclusion we give some examples.
This work was supported by CNR and M.U.R.S.T. 相似文献
13.
The theory of the 1-inverse of a matrix is used to derive allsymmetric updates which satisfy a matrix equation. This generalsolution is then used to obtain the solution which is minimumin a symmetrically weighted Frobenius norm. The minimum normsolution can be used to derive the minimum norm updates usedin quasi-Newton methods for unconstrained optimization.
This research was supported in part by NIH Grant No. AM17593. 相似文献
14.
In this paper we analyze the use of a combined Nystrm and finite-elementprocedure for approximating the scattered time-harmonic acousticfield produced when an incident wave interacts with a boundedinhomogeneity. The coupling technique uses a smooth artificialboundary and explicitly decouples the integral equation andfinite-element computations. We prove convergence of the method.One highlight of this analysis is that we prove Sobolev spaceerror estimates for the Nystrm scheme (which is usually analyzedin Hlder spaces). We also present some numerical results.
E-mail: kirsch{at}am.uni-erlangen.de
E-mail: monk{at}math.udel.edu 相似文献
15.
In a recent paper, Fischer and Finn have proposed a procedureto improve the accuracy in the measurement of capillary contactangles, based on the use of vessels with canonical cross-sections.We simulate numerically the behaviour of such shapes for a numberof cross-sections and fluid contact angles. Our approximationconsists of the minimization of a suitable convex functionaldiscretized by finite elements.
e-mail: bellettini{at}sns.it
e-mail: paolini{at}isa.mat.unimi.it 相似文献
16.
In a recent paper Fox & Mayers discuss the numerical solutionof implicit ordinary differential equations of the form f(x,y(x), y'(x)) = 0. They find that numerical methods can be veryunreliable near the point where fy' = 0. In this paper we givea theoretical analysis of the problem which enables us to explainwhen to expect numerical difficulties. We suggest a possibleline of approach for the solution of such problems, and discusssome numerical examples.
Research supported by the National Science Foundation, the Officeof Naval Research, the Army Research, and the Air Force Officeof Scientific Research. Travel funding provided by the Universityof Toronto and the British Council. 相似文献
17.
The stability of nonautonomous delay differential equationsis studied via a combination of the global linerization andnonlinear variation of parameter techniques.
Permanent address: Department of Mathematics, University ofElectronics Science & Technology of China, Chengdu, China. 相似文献
18.
Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems 总被引:2,自引:0,他引:2
The long-time behaviour of continuous time Galerkin (CTG) approximationsof some well-known one-dimensional non-linear evolution problemswhich model phase transitions are analyzed. These numericalschemes are fully discrete and of arbitrary order.
Partially supported by the Army Research Office through grant28535-MA.
Partially supported by the ONR Contract No N00014-90-J-1238. 相似文献
19.
We study a boundary integral equation method for solving Laplace'sequation u=0 with non-linear boundary conditions. This non-linearboundary value problem is reformulated as a non-linear boundaryintegral equation, with u on the boundary as the solution beingsought. The integral equation is solved numerically by usingthe collocation method, with piecewise quadratic functions usedas approximations to u. Convergence results are given for thecases where (1) the original surface is used, and (2) the surfaceis approximated by piecewise quadratic interpolation. In addition,we define and analyze a two-grid iteration method for solvingthe non-linear system that arises from the discretization ofthe boundary integral equation. Numerical examples are given;and the paper concludes with a short discussion of the relativecost of different parts of the method.
This work was supported in part by NSF grant DMS-9003287. 相似文献
20.
This paper provides characterizations of the Pareto distributionof the second kind, the Pearson type-VII distribution and thet-distribution. These characterizations have been obtained throughmaximization of -entropies. As 1, characterizations of the exponential,the Laplace, and the normal distributions are obtained.
On sabbatical leave from the Department of Statistics, YarmoukUniversity, Irbid, Jordan. 相似文献