New methods for solving elliptic equations

by J. N Vekua

Publisher: North-Holland Pub. Co. in Amsterdam

Written in English
Published: Pages: 358 Downloads: 625
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Subjects:

  • Differential equations, Elliptic

Edition Notes

SeriesNorth-Holland series in applied mathematics and mechanics -- v. 1
Classifications
LC ClassificationsQA374 V383
The Physical Object
Pagination358p.
Number of Pages358
ID Numbers
Open LibraryOL17481609M

non-time matching nature of elliptic equations, we often refer to them as diagnostic equations. Methods for Solving Elliptic Equations Introduction Many methods exist, some of them are available as 'canned' programs in standard libraries, such as IMSL. Commonly used methods can be divided into the following classes: a. paper, a new class of high order finite volume methods for second order elliptic equations is developed by combining high order finite element methods and linear finite volume methods. Optimal convergence rate in H1-norm for our new quadratic finite volume methods over two dimensional triangular or rectangular grids is obtained. Key words. Numerical methods for elliptic partial differential equations have been the subject of many books in recent years, but few have treated the subject of complex equations. In this important new book, the author introduces the theory of, and approximate methods for, nonlinear elliptic complex equations in multiple connected domains. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations.3/5(1).

The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems. This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations by Beatrice M. Riviere, , available at Book Depository with free delivery worldwide. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.

One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized. Growth of computing power and the importance of algorithms 1 10 CPU speed Year Problem size YYearear Consider the computational task of solving a linear system A u = b of N algebraic equations with N unknowns. Classical methods such as Gaussian elimination require O(N3) operations. Using an O(N3) method, an increase in computing power by a factor of finite element methods. Sobolev Spaces and Theory on Elliptic Equations. Sobolev spaces are fundamen-tal in the study of partial differential equations and their numerical approximations. The regularity theory for elliptic boundary value problems plays an important role in .

New methods for solving elliptic equations by J. N Vekua Download PDF EPUB FB2

Additional Physical Format: Online version: Vekua, I.N. (Ilʹi︠a︡ Nestorovich), New methods for solving elliptic equations. Amsterdam: North-Holland. New Methods for Solving Elliptic Equations (North-Holland Series in Applied Mathematics & Mechanics) Hardcover – Import, by I.N. Vekua (Author) See all formats and editions Hide other formats and editions.

Price New from Author: I.N. Vekua. New methods for solving elliptic equations () by I N Vekua Add To MetaCart.

Tools. Sorted by can be used to employ the structure of the differential equation under consideration to construct effective and robust methods. Although the method and its theory are valid in n dimensions, a detailed and illustrative analysis will be given for.

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow.

The book also tackles the numerical solution of a model equation near the onset of the Rayleigh-Benard instability; numerical methods for solving coupled semiconductor equations on a minicomputer; and analysis of nonlinear elliptic systems arising in reaction/diffusion modeling. Qualitative behavior.

Elliptic equations have no real characteristic curves, curves along which it is not possible to eliminate at least one second derivative of from the conditions of the Cauchy problem.

Since characteristic curves are the only curves along which solutions to New methods for solving elliptic equations book differential equations with smooth parameters can have discontinuous derivatives, solutions to elliptic.

Book Title New methods for solving elliptic equations: Author(s) Vekua, I N: CERN Document Server Access articles, reports and multimedia content in HEP. Main menu Discussion (0) Files ; Holdings.

Book Title New methods for solving elliptic equations: Author(s) Vekua, I N: Publication Amsterdam: North-Holland, - p.

Series. New to the Second Edition More than 1, pages with over 1, new first- second- third- fourth- and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM.

Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience.

non-time matching nature of elliptic equations, we often refer to them as diagnostic equations. Methods for Solving Elliptic Equations Introduction Many methods exist, some of them are available as 'canned' programs in standard libraries, such as IMSL.

Commonly used methods can be divided into the following classes: Size: 75KB. A multidomain spectral method for solving elliptic equations Harald P. Pfei er, Lawrence E.

Kiddery, Mark A. Scheelz, and Saul A. Teukolsky x Department of Physics, Cornell University, Ithaca, New Yorky Center for Radiophysics and Space Research, Cornell University, Ithaca, New York.

Some 15–20 years ago, there was considerable interest in iterative methods for the solution of elliptic difference equations. The interest in finite-element techniques and direct methods for the solution of large sparse systems reduced interest in iterative methods. We propose, analyze, and illustrate a ‘spectral method’ for solving numerically such an eigenvalue problem.

This is an extension of the methods presented earlier in [5], [6]. Key words. elliptic equations, eigenvalue problem, spectral method, multivariable approxima-tion AMS subject classification. 65M70 1. INTRODUCTION.

Discontinous Galerkin (DG) methods for solving partial differential equations, developed in the late s, have become popular among computational scientists.

Covering both theory and computation, this book focuses on three primal DG methods - the symmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and nonsymmetric Cited by:   Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late s, have become popular among computational scientists.

This book covers both theory and computation as it focuses on three primal DG methods?the symmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and nonsymmetric interior penalty Galerkin?which are variations. This book presents finite difference methods for solving partial differential equations (PDEs) and also general concepts like stability, boundary conditions etc.

Material is in order of increasing complexity (from elliptic PDEs to hyperbolic systems) with related theory included in appendices/5(17). SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () A level set-based immersed interface method for solving incompressible viscous flows with the prescribed velocity at Cited by: Nečas’ book Direct Methods in the Theory of Elliptic Equations, published in French, has become a standard reference for the mathematical theory of linear elliptic equations and English edition, translated by G.

Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in   Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book.

on a very small scale. The aim of this thesis is to construct practical numerical methods for solving these equations. The main results presented in this thesis are also available in [3, 20]. The Monge-Amp ere Equation The Monge-Amp ere equation is a fully nonlinear elliptic PDE which is closely related to im-Author: Brittany Dawn Froese.

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. Abstract. A new method for solving boundary value problems has recently been introduced by the first author.

Although this method was first developed for non-linear integrable PDEs (using the crucial notion of a Lax pair), it has also given rise to new analytical and numerical techniques for linear we review the application of the new method to linear elliptic PDEs, using the.

Solving the Poisson equation. ij using new values as soon as they become available. j-1. j+1. i-1. i!i+1.

for j=1:m for i=1:n iterate end end Examples of elliptic equations. Direct Methods for 1D problems. Elementary Iterative Methods. Iteration as Time Integration. Example. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

() Analysis of two-grid method for semi-linear elliptic equations by new mixed finite element scheme. Applied Mathematics and Computation() Some iterative finite element methods for steady Navier–Stokes equations with different by: The main idea of this book is to introduce the main concepts and results of wavelet methods for solving linear elliptic partial differential equations in a framework that allows avoiding Author: Karsten Urban.

Discontinuous Galerkin Methods For Solving Elliptic And parabolic Equations: Theory and is a successful alternative for modeling some types of partial differential equations (PDEs). This book balances between the pedagogic and the cutting edge of applied mathematics for this particular subject.

or even wanting to delve into some new. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation (Frontiers in Applied Mathematics) by Rivière, Béatrice M.

and a great selection of related books, art and collectibles available now at elliptic. To do so, use the results given in Brenner and Scott [6, §§], combined with the methods of the present paper.

We have chosen to restrict our work to the more standard symmetric problem (1). There is a rich literature on spectral methods for solving partial di⁄erential equations. Complex Variables and Elliptic Equations: An International Journal ( - current) Formerly known as.

Complex Variables, Theory and Application: An International Journal ( - ) Latest articles. pages pages pages Functional Analytic Methods in Partial Differential Equations. pages x. LECTURE SLIDES LECTURE NOTES; Numerical Methods for Partial Differential Equations ()(PDF - MB)Finite Difference Discretization of Elliptic Equations: 1D Problem ()(PDF - MB)Finite Difference Discretization of Elliptic Equations: FD Formulas and Multidimensional Problems ()(PDF - MB)Finite Differences: Parabolic Problems ()(Solution Methods: Iterative Techniques ().• Fast methods for linear algebra (solve Ax = b in O(N) time for A dense N × N matrix).

Existing methods (fast multipole methods, etc) can be accelerated. Parallel implementations. • Techniques for discretizing equations — tricky since the kernel is singular. • Techniques for File Size: 2MB.Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions Article (PDF Available) in SIAM Journal on Scientific Computing 40(4):BB January with 52 Reads.