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Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes

Communications in Computational Physics 2011年第3期9卷 520-541页

作者： Steven Britt Semyon Tsynkov Eli Turkel Department of Mathematics North Carolina State UniversityBox 8205RaleighNC 27695USA School of Mathematical Sciences Tel Aviv UniversityRamat AvivTel Aviv 69978Israel

In many problems,one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method(e.g.,fourth order accurate)to alleviate the points-per-wavelength constraint by reducing the dispersion *** variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian *** renders existing fourth order finite difference methods *** develop a new compact scheme that is provably fourth order accurate even for these *** present numerical results that corroborate the fourth order convergence rate for several model problems.

关键词： Helmholtz equation variable coefficients high order accuracy compact finite differences

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HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS

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International Journal of Modeling, Simulation, and Scientific Computing 2012年第2期3卷 1-18页

作者： R.K.MOHANTY VENU GOPAL Department of Mathematics University of Delhi Delhi-110007India

In this paper,we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyper-bolic partial differential equation of the form utt=A(x,y,t)uxx+B(x,y,t)uyy+g(x,y,t,u,ux,uy,ut),00 subject to appropriate initial and Dirichlet boundary *** use only five evaluations of the function g and do not require any fictitious points to discretize the differential *** proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally *** results are provided to illustrate the usefulness of the proposed method.

关键词： Nonlinear hyperbolic equation variable coefficients arithmetic average type approximation wave equation in polar coordinates van der Pol equation telegraphic equation maximum absolute errors.

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A Matrix-Vector Operation-Based Numerical Solution Method for Linear m-th Order Ordinary Differential Equations:Application to Engineering Problems

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Advances in Applied Mathematics and Mechanics 2013年第3期5卷 269-308页

作者： M.Aminbaghai M.Dorn J.Eberhardsteiner B.Pichler Institute for Mechanics of Materials and Structures Vienna University of Technology(TU Wien)Karlsplatz 13/202A-1040 ViennaAustria Linnaeus University Department of Building and Energy TechnologyL¨uckligs Plats 1S-35195 V¨axj¨oSweden

Many problems in engineering sciences can be described by linear,inhomogeneous,m-th order ordinary differential equations(ODEs)with variable *** this wide class of problems,we here present a new,simple,flexible,and robust solution method,based on piecewise exact integration of local approximation polynomials as well as on averaging local *** method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based *** on cubic approximation polynomials,the presented method can be expected to perform(i)similar to the Runge-Kutta method,when applied to stiff initial value problems,and(ii)significantly better than the finite difference method,when applied to boundary value ***,we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum,steady-state heat transfer through a cooling web,and the structural analysis of a slender tower based on second-order beam *** convergence studies provide insight into the satisfying characteristics of the proposed solution scheme.

关键词： Numerical integration polynomial approximation ODE variable coefficients initial conditions boundary conditions stiff equation

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A General Solution for Trinomial Linear Recurrence with Two Indices

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Wuhan University Journal of Natural Sciences 2011年第3期16卷 190-192页

作者： YU Chang'an School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China

In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete ... 详细信息

关键词： a formula of general solution homogeneous trinomial recurrence variable coefficients two indices

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An Explicit Solution for a Special Class of Homogeneous Recurrence with Two Indices

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Wuhan University Journal of Natural Sciences 2003年第2A期8卷 342-346页

作者： YuChang-an YuDan SchoolofMathematicsandStatisticsScience WuhanUniversityWuhan430072HubeiChina SchoolofComputer WuhanUniversityWuhan430072HubeiChina

On the basis of author's former work,an explicit solution for a special class of homogeneous recurrence with two indices has been derived. It provides a concrete model to solve the concernced problems with computer. T... 详细信息

关键词： two indices variable coefficients homogeneous recurrence an explicit solution

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