Third and Fourth Order Accuracy Schemes for Two Dimensional Hyperbolic Equations PDF Download
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Author: Gideon Zwas Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
In this paper the Lax-Wendroff procedure is extended to the scalar case of a two-dimensional hyperbolic conservation law. Explicit third and fourth order accuracy finite-difference operators are constructed for solving quasi-linear initial value problems. Stability conditions are obtained and are used in numerical computations. The computational results which are presented demonstrate that large amounts of computing time and memory space are saved without loss of accuracy. (Author).
Author: S. Abarbanel Publisher: ISBN: Category : Languages : en Pages : 55
Book Description
Two explicit finite difference schemes of fourth order accuracy (in space and time) are presented for the numerical solution of quasi-linear divergence free one dimensional hyperbolic systems. Both of these schemes are four step methods, one being a two level scheme, the other using three levels. These algorithms are compared in numerical examples with both second order schemes and with the DREISS-OLIGER method which is fourth order in space and second order in time. The results show that it is most advantageous to use the true fourth order schemes. (Author).
Author: Gideon Zwas Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
In this paper the Lax-Wendroff procedure is extended to the scalar case of a two-dimensional hyperbolic conservation law. Explicit third and fourth order accuracy finite-difference operators are constructed for solving quasi-linear initial value problems. Stability conditions are obtained and are used in numerical computations. The computational results which are presented demonstrate that large amounts of computing time and memory space are saved without loss of accuracy. (Author).
Author: Svetozar Margenov Publisher: Springer Science & Business Media ISBN: 3642004636 Category : Computers Languages : en Pages : 646
Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.
Author: Sergey Lemeshevsky Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110489724 Category : Mathematics Languages : en Pages : 265
Book Description
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Author: Bertil Gustafsson Publisher: Springer Science & Business Media ISBN: 3540749934 Category : Mathematics Languages : en Pages : 343
Book Description
This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.
Author: A.G. Kulikovskii Publisher: CRC Press ISBN: 1482273993 Category : Mathematics Languages : en Pages : 560
Book Description
This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics,
Author: Publisher: ISBN: Category : Languages : en Pages : 18
Book Description
It is shown that for quasi-linear hyperbolic systems of the conservation form W sub t = -(F sub x) = -A(W sub x), it is possible to build up relatively simple finite difference numerical schemes accurate to 3rd and 4th order provided that the matrix A satisfies commutativity relations with its partial-derivative-matrices. This requirement is not fulfilled by any known physical systems of equations. These schemes generalize the Lax-Wendroff 2nd order one, and are written down explicitly. As found by Strang, odd order schemes are linearly unstable unless modified by adding a term containing the next higher space derivative. Thus stabilized, the schemes, both odd and even, can be made to meet the C.F.L. (Courant-Friedrichs-Lewy) criterion. Numerical calculations were made with a 3rd order and a 4th order scheme for scalar equations with continuous and discontinuous solutions. The results are compared with analytic solutions and the predicted improvement is verified.
Author: Gideon Zwas
Author: S. Abarbanel
Author: Gideon Zwas
Author: Peter D. Lax
Author: Svetozar Margenov
Author: Sergey Lemeshevsky
Author: Bertil Gustafsson
Author: Christopher A. Kennedy
Author: A.G. Kulikovskii
Author: John C. Strikwerda
Author: