Numerical Methods for Grid Equations

Numerical Methods for Grid Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 292
Release :
ISBN-10 : 3764322764
ISBN-13 : 9783764322762
Rating : 4/5 (64 Downloads)

Synopsis Numerical Methods for Grid Equations by : A.A. Samarskij

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.

Numerical Methods for Grid Equations

Numerical Methods for Grid Equations
Author :
Publisher : Birkhäuser
Total Pages : 273
Release :
ISBN-10 : 9783034892728
ISBN-13 : 3034892721
Rating : 4/5 (28 Downloads)

Synopsis Numerical Methods for Grid Equations by : A.A. Samarskij

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.

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 437
Release :
ISBN-10 : 9780387954493
ISBN-13 : 038795449X
Rating : 4/5 (93 Downloads)

Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner

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.

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations
Author :
Publisher : Academic Press
Total Pages : 484
Release :
ISBN-10 : 9780128035047
ISBN-13 : 0128035048
Rating : 4/5 (47 Downloads)

Synopsis Numerical Methods for Partial Differential Equations by : Sandip Mazumder

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

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 775
Release :
ISBN-10 : 9783540772095
ISBN-13 : 354077209X
Rating : 4/5 (95 Downloads)

Synopsis Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by : Tarek Mathew

Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

Numerical Analysis of Partial Differential Equations

Numerical Analysis of Partial Differential Equations
Author :
Publisher : John Wiley & Sons
Total Pages : 506
Release :
ISBN-10 : 9781118111116
ISBN-13 : 1118111117
Rating : 4/5 (16 Downloads)

Synopsis Numerical Analysis of Partial Differential Equations by : S. H, Lui

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Numerical Methods for Grid Equations

Numerical Methods for Grid Equations
Author :
Publisher :
Total Pages : 300
Release :
ISBN-10 : 0817630996
ISBN-13 : 9780817630997
Rating : 4/5 (96 Downloads)

Synopsis Numerical Methods for Grid Equations by : A. A. Samarskii

Numerical Analysis

Numerical Analysis
Author :
Publisher : SIAM
Total Pages : 448
Release :
ISBN-10 : 9781611975703
ISBN-13 : 1611975700
Rating : 4/5 (03 Downloads)

Synopsis Numerical Analysis by : Brian Sutton

This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.

The Numerical Solution of Integral Equations of the Second Kind

The Numerical Solution of Integral Equations of the Second Kind
Author :
Publisher : Cambridge University Press
Total Pages : 572
Release :
ISBN-10 : 9780521583916
ISBN-13 : 0521583918
Rating : 4/5 (16 Downloads)

Synopsis The Numerical Solution of Integral Equations of the Second Kind by : Kendall E. Atkinson

This book provides an extensive introduction to the numerical solution of a large class of integral equations.

Introduction to Numerical Geodynamic Modelling

Introduction to Numerical Geodynamic Modelling
Author :
Publisher : Cambridge University Press
Total Pages : 359
Release :
ISBN-10 : 9780521887540
ISBN-13 : 0521887542
Rating : 4/5 (40 Downloads)

Synopsis Introduction to Numerical Geodynamic Modelling by : Taras Gerya

This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.