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).
Difference Schemes with Fourth Order Accuracy for Hyperbolic Equations
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).
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).
Third and Fourth Order Accuracy Schemes for Two Dimensional Hyperbolic Equations
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).
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).
Difference Schemes with High Order of Accuracy for Solving Hyperbolic Equations
Author: Peter D. Lax
Publisher:
ISBN:
Category : Differential-difference equations
Languages : en
Pages : 62
Book Description
Publisher:
ISBN:
Category : Differential-difference equations
Languages : en
Pages : 62
Book Description
Exact Finite-Difference Schemes
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
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
Numerical Analysis and Its Applications
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.
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.
High Order Difference Methods for Time Dependent PDE
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.
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.
Asymptotic Analysis
Author: Mikhail V. Fedoryuk
Publisher: Springer Science & Business Media
ISBN: 3642580165
Category : Mathematics
Languages : en
Pages : 370
Book Description
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Publisher: Springer Science & Business Media
ISBN: 3642580165
Category : Mathematics
Languages : en
Pages : 370
Book Description
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers
Author: Christopher A. Kennedy
Publisher:
ISBN:
Category : Finite differences
Languages : en
Pages : 66
Book Description
Publisher:
ISBN:
Category : Finite differences
Languages : en
Pages : 66
Book Description
Mathematical Aspects of Numerical Solution of Hyperbolic Systems
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,
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,
Finite Difference Schemes and Partial Differential Equations
Author: John C. Strikwerda
Publisher: SIAM
ISBN: 089871639X
Category : Mathematics
Languages : en
Pages : 439
Book Description
A unified and accessible introduction to the basic theory of finite difference schemes.
Publisher: SIAM
ISBN: 089871639X
Category : Mathematics
Languages : en
Pages : 439
Book Description
A unified and accessible introduction to the basic theory of finite difference schemes.