Numerical Methods For Solving Linear Systems And Applications To Elliptic Difference Equations

Author : Clarence Edgar Lee
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.96/5 ( download)

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Download or read book Numerical Methods for Solving Linear Systems and Applications to Elliptic Difference Equations written by Clarence Edgar Lee and published by . This book was released on 1959 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative numerical methods for solving independent, simultaneous, inhomogeneous linear equations are surveyed. Application of the methods to elliptic difference equations as arise in neutron diffasion, heat conduction, and potential problems is discussed.

Author : Peter Knabner
Publisher : Springer Science & Business Media
ISBN 13 : 0387217622
Total Pages : 437 pages
Book Rating : 4.28/5 ( download)

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Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jichun Li
Publisher : CRC Press
ISBN 13 : 0429556535
Total Pages : 423 pages
Book Rating : 4.31/5 ( download)

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Download or read book Computational Partial Differential Equations Using MATLAB® written by Jichun Li and published by CRC Press. This book was released on 2019-09-26 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.

Author : W. Hackbusch
Publisher : Springer Science & Business Media
ISBN 13 : 9783540548225
Total Pages : 334 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Elliptic Differential Equations written by W. Hackbusch and published by Springer Science & Business Media. This book was released on 1992 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR

Author : Wolfgang Hackbusch
Publisher : Springer
ISBN 13 : 3662549611
Total Pages : 455 pages
Book Rating : 4.12/5 ( download)

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Download or read book Elliptic Differential Equations written by Wolfgang Hackbusch and published by Springer. This book was released on 2017-06-01 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Author : Guri I Marchuk
Publisher : CRC Press
ISBN 13 : 135135969X
Total Pages : 220 pages
Book Rating : 4.96/5 ( download)

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Download or read book Numerical Methods and Applications (1994) written by Guri I Marchuk and published by CRC Press. This book was released on 2017-11-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gerard Meurant
Publisher : Elsevier
ISBN 13 : 0080529518
Total Pages : 777 pages
Book Rating : 4.16/5 ( download)

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Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Author : Donald Greenspan
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.42/5 ( download)

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Download or read book Lectures on the Numerical Solution of Linear, Singular, and Nonlinear Differential Equations written by Donald Greenspan and published by Prentice Hall. This book was released on 1968 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Marián Vajtersic
Publisher : Springer Science & Business Media
ISBN 13 : 9401707014
Total Pages : 310 pages
Book Rating : 4.15/5 ( download)

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Download or read book Algorithms for Elliptic Problems written by Marián Vajtersic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems. The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems. For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.

Author : Garrett Birkhoff
Publisher : SIAM
ISBN 13 : 0898710014
Total Pages : 93 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Numerical Solution of Elliptic Equations written by Garrett Birkhoff and published by SIAM. This book was released on 1971-01-01 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.