Author: A.A. Samarskij
Publisher: Birkhäuser
ISBN: 9783764322786
Category : Mathematics
Languages : en
Pages :

Get Book Here

Book Description

Author: A.A. Samarskij
Publisher: Birkhäuser
ISBN: 3034892721
Category : Mathematics
Languages : en
Pages : 273

Get Book Here

Book Description
The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes.

Author: A.A. Samarskij
Publisher: Birkhäuser
ISBN: 9783034891431
Category : Mathematics
Languages : en
Pages : 502

Get Book Here

Book Description

Author: Aleksandr Andreevich Samarskiĭ
Publisher: Birkhauser
ISBN: 9780817622763
Category : Mathematics
Languages : en
Pages : 242

Get Book Here

Book Description

Author: A. A. Samarskii
Publisher:
ISBN: 9780817630997
Category :
Languages : en
Pages : 300

Get Book Here

Book Description

Author: Aleksandr A. Samarskii
Publisher:
ISBN: 9780817622770
Category : Differential equations
Languages : en
Pages : 501

Get Book Here

Book Description

Author: Dale R. Durran
Publisher: Springer Science & Business Media
ISBN: 1441964126
Category : Mathematics
Languages : en
Pages : 527

Get Book Here

Book Description
This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

Author: Guri I Marchuk
Publisher: CRC Press
ISBN: 1351359703
Category : Mathematics
Languages : en
Pages : 282

Get Book Here

Book Description
This book presents new original numerical methods that have been developed to the stage of concrete algorithms and successfully applied to practical problems in mathematical physics. The book discusses new methods for solving stiff systems of ordinary differential equations, stiff elliptic problems encountered in problems of composite material mechanics, Navier-Stokes systems, and nonstationary problems with discontinuous data. These methods allow natural paralleling of algorithms and will find many applications in vector and parallel computers.

Author: Peter Knabner
Publisher: Springer Science & Business Media
ISBN: 038795449X
Category : Mathematics
Languages : en
Pages : 437

Get Book Here

Book Description
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Author: Sandip Mazumder
Publisher: Academic Press
ISBN: 0128035048
Category : Mathematics
Languages : en
Pages : 484

Get Book Here

Book Description
Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives