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Transformations of Difference Equations II

ADVANCES IN DIFFERENCE EQUATIONS 2010年第1期2010卷 623508-623508页

作者： Currie, Sonja Love, Anne D. Univ Witwatersrand Sch Math ZA-2050 Wits South Africa

This is an extension of the work done by Currie and Love (2010) where we studied the effect of applying two Crum-type transformations to a weighted second-order difference equation with non-eigenparameter-dependent boundary conditions at the end points. In particular, we now consider boundary conditions which depend affinely on the eigenparameter together with various combinations of Dirichlet and non-Dirichlet boundary conditions. The spectra of the resulting transformed boundary value problems are then compared to the spectra of the original boundary value problems.

关键词： DIFFERENCE equations -- numerical solutions TRANSFORMATIONS (Mathematics) PARAMETER estimation boundary value problems -- numerical solutions DIRICHLET problem -- numerical solutions COMBINATIONS (Mathematics) COMPARATIVE studies

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Regularity of Weakly Well-Posed Characteristic boundary value problems

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INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS 2010年第unknown期2010卷 1-39页

作者： Morando, Alessandro Secchi, Paolo Univ Brescia Fac Ingn Dipartimento Matemat Via Valotti 9 I-25133 Brescia Italy

We study the boundary value problem for a linear first-order partial differential system with characteristic boundary of constant multiplicity. We assume the problem to be "weakly" well posed, in the sense that a unique L-2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of tangential/conormal regularity. This is the case of problems that do not satisfy the uniform Kreiss-Lopatinski. i condition in the hyperbolic region of the frequency domain. Provided that the data are sufficiently smooth, we obtain the regularity of solutions, in the natural framework of weighted conormal Sobolev spaces.

关键词： boundary value problems -- numerical solutions EXTERIOR differential systems ISOMORPHISMS (Mathematics) SOBOLEV spaces DIFFERENTIAL equations -- numerical solutions PSEUDODIFFERENTIAL operators

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Infinitely Many solutions for a Robin boundary value Problem

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INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS 2010年第unknown期2010卷 1-9页

作者： Qian, Aixia Li, Chong Qufu Normal Univ Sch Math Sci Qufu 273165 Shandong Peoples R China Acad Sinica AMSS Inst Math Beijing 100080 Peoples R China

By combining the embedding arguments and the variational methods, we obtain infinitely many solutions for a class of superlinear elliptic problems with the Robin boundary value under weaker conditions.

关键词： DIRICHLET problem NEUMANN problem boundary value problems -- numerical solutions SOBOLEV spaces MEASURE theory DIFFERENTIAL equations

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Hall effects on hydromagnetic flow of an Oldroyd 6-constant fluid between concentric cylinders

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CHAOS SOLITONS & FRACTALS 2009年第1期39卷 204-213页

作者： Rana, M. A. Siddiqui, A. M. Qamar, Rashid PINSTECH Management Informat Syst Islamabad 44000 Pakistan Penn State Univ Dept Math York PA 17403 USA

The hydromagnetic flow of an electrically conducting, incompressible Oldroyd 6-constant fluid between two concentric cylinders is investigated. The flow is generated by moving inner cylinder and/or application of the constant pressure gradient. Two non-linear boundary value problems are solved numerically. The effects of material parameters, pressure gradient, magnetic field and Hall parameter on the velocity are studied. The graphical representation of velocity reveals that characteristics for shear thinning/shear thickening behaviour of a fluid is dependent upon the rheological properties. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： HALL effect MAGNETOHYDRODYNAMICS ELECTRIC conductivity SHEAR flow boundary value problems -- numerical solutions MAGNETIC fields

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B-spline solution of a singularly perturbed boundary value problem arising in biology

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CHAOS SOLITONS & FRACTALS 2009年第5期42卷 2934-2948页

作者： Lin, Bin Li, Kaitai Cheng, Zhengxing Xi An Jiao Tong Univ Coll Sci Xian 710049 Peoples R China

We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： boundary value problems -- numerical solutions SPLINE theory PERTURBATION (Mathematics) BIOLOGICAL mathematical modeling SINGULARITIES (Mathematics) LINEAR systems COLLOCATION methods FUNCTIONS (Mathematics)

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A parallel boundary fitted dynamic mesh solver for applications to flapping flight

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COMPUTERS & FLUIDS 2009年第8期38卷 1592-1607页

作者： Gopalakrishnan, Pradeep Tafti, Danesh K. Virginia Polytech Inst & State Univ Blacksburg VA 24061 USA

A parallel numerical solution procedure for unsteady incompressible flow is developed for simulating the dynamics of flapping flight. A collocated finite volume multiblock approach in a general curvilinear coordinate is used with Cartesian velocities and pressure as dependent variables. The Navier-Stokes equations are solved using a fractional-step algorithm. The dynamic grid algorithm is implemented by satisfying the space conservation law by computing the grid velocities in terms of the volume swept by the faces. The dynamic movement of grid in a multiblock approach is achieved by using a combination of spring analogy and Trans-Finite Interpolation. The spring analogy is used to compute the displacement of block corners, after which Trans-Finite Interpolation is applied independently on each computational block. The performance of the code is validated in forced transverse oscillations of a cylinder in cross-flow, a heaving airfoil, and hovering of a fruitfly. Finally, the unsteady aerodynamics of flapping flight at Re = 10,000 relevant to the development of Micro Air Vehicles is analyzed for forward flight. The results show the capability of the solver in predicting unsteady aerodynamics characterized by complex boundary movements. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： numerical analysis numerical grid generation (numerical analysis) PARTIAL differential equations -- numerical solutions boundary value problems -- numerical solutions

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On the spectrum of a nonlinear planar problem

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ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE 2009年第1期26卷 191-222页

作者： Gladiali, Francesca Grossi, Massinio Univ Roma La Sapienza Dipartimento Matemat I-00185 Rome Italy Univ Sassari Struttura Dipartimentale Matemat & Fis I-07100 Sassari Italy

We consider the eigenvalue problem [GRAPHICS] where Omega is a bounded smooth domain of R-2, lambda > 0 is a real parameter and it is a solution of [GRAPHICS] such that lambda integral Omega EU lambda -> 8 pi as lambda -> 0. In this paper we Study theasymptotic behavior of the eigenvalues mu of(0, 1) as lambda -> 0. Moreover some explicit estimates for the four first eigenvalues and eigenfunctions are given. Other related results as the Morse index of the solution u(lambda) will be proved. (c) 2007 Flsevier Masson SAS. All rights reserved.

关键词： EIGENvalueS MATRICES EIGENFUNCTIONS boundary value problems -- numerical solutions

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Identification of the Cooling Condition in 2-D and 3-D Continuous Casting Processes

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2009年第2期55卷 155-176页

作者： Slota, Damian Silesian Tech Univ Inst Math PL-44100 Gliwice Poland

In this article, the reconstruction of the function describing the boundary conditions along the primary and secondary cooling zones in the 2-D and 3-D continuous casting processes of pure metal is presented. The process is modeled by the inverse Stefan problem, where additional information consists of temperature measurements at selected points of the domain. In numerical calculations, Tikhonov's regularization, a genetic algorithm, and an alternating phase truncation method are used. The featured examples of calculations show very good approximation of the exact solution. The influence of the number and accuracy of measurements are also investigated.

关键词： CONTINUOUS casting THERMOPHYSICAL properties GENETIC algorithms RESEARCH THERMAL conductivity measurement boundary value problems -- numerical solutions SOLIDIFICATION

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BILINEARIZATION APPROACH FOR DIFFUSION problems INVOLVING THE CALCULATION OF DISSIPATIVE FIELDS

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2009年第6期55卷 457-479页

作者： Mathieu-Potvin, Francois Gosselin, Louis Univ Laval Dept Genie Mecan Quebec City PQ GIV 0A6 Canada

A straightforward procedure is developed to determine dissipation fields (e. g., exergy destruction in conduction, pumping power, Joule heating) from the linear boundary conditions applied on their associated linear diffusion problem (e. g., heat conduction, Darcy flow, electrical flow). The mathematical tool proposed in this article takes advantage of the quadratic (nonlinear) behavior that comes with dissipative fields equations. The first objective of this article is to build a mathematical formulation expressing any dissipation field as a combination of fundamental dissipative fields resulting from decomposed boundary conditions, similarly to linear problems where fundamental solutions may be added with the superposition principle. The second objective is to demonstrate the numerical advantage of this formulation when applied to heat transfer and fluid flow optimization problems. Application of the mathematical tool proposed in this article to boundary control problems provided significant computational time reductions.

关键词： HEAT transfer RESEARCH FLUID dynamics THERMAL conductivity HEAT conduction boundary value problems -- numerical solutions PERMEABILITY JOULE-Thomson effect

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Meshless Method for Geometry boundary Identification Problem of Heat Conduction

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2009年第2期55卷 135-154页

作者： Tan, J. Y. Zhao, J. M. Liu, L. H. Harbin Inst Technol Sch Energy Sci & Engn Harbin 150001 Peoples R China Harbin Inst Technol Weihai Sch Auto Engn Weihai Peoples R China

A geometry identification problem of two-dimensional heat conduction is solved by using the least-squares collocation meshless method and the conjugate gradient method. In the least-squares collocation meshless approach for solving the direct heat conduction problem, a number of collocation points and auxiliary points are used to discretize the problem domain, and the collocation points are taken to construct the trial function by moving least-squares approximation. Akima cubic interpolation is employed to transform the geometry boundary inverse problem to the discrete boundary point's inverse problem and approximate the unknown boundary in an inverse iterative process. In order to illustrate the performance and verify the new solution method, four typical cases are considered. The numerical results show that the least-squares collocation meshless method combined with the conjugate gradient method is accurate and stable for solving the geometry identification problem of heat conduction.

关键词： THERMAL conductivity measurement boundary value problems -- numerical solutions LEAST squares MESHFREE methods (numerical analysis) CONJUGATE gradient methods INVERSE problems (Differential equations) -- numerical solutions

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