Download or read book A Method of Integration Over the Boundary for Solving Boundary Value Problems written by Paul Shuleshko and published by . This book was released on 1960 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Unified Approach to Boundary Value Problems written by Athanassios S. Fokas and published by SIAM. This book was released on 2008-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Download or read book Mixed Boundary Value Problems written by Dean G. Duffy and published by CRC Press. This book was released on 2008-03-26 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for Solving Mixed Boundary Value Problems An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equat
Download or read book A Beginner s Course in Boundary Element Methods written by Whye-Teong Ang and published by Universal-Publishers. This book was released on 2007 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a course in boundary element methods for the absolute beginners. Basic concepts are carefully explained through the use of progressively more complicated boundary value problems in engineering and physical sciences. The readers are assumed to have prior basic knowledge of vector calculus (covering topics such as line, surface and volume integrals and the various integral theorems), ordinary and partial differential equations, complex variables, and computer programming. Electronic ebook edition available at Powells.com. Click on Powells logo to the left.
Download or read book Boundary Value Problems For Analytic Functions written by Jian-ke Lu and published by World Scientific. This book was released on 1994-02-04 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincaré-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
Download or read book Natural Boundary Integral Method and Its Applications written by De-hao Yu and published by Springer Science & Business Media. This book was released on 2002-09-30 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary element methods are very important for solving boundary value problems in PDEs. Many boundary value problems of partial differential equations can be reduced into boundary integral equations by the natural boundary reduction. In this book the natural boundary integral method, suggested and developed by Feng and Yu, is introduced systematically. It is quite different from popular boundary element methods and has many distinctive advantages. The variational principle is conserved after the natural boundary reduction, and some useful properties are also preserved faithfully. Moreover, it can be applied directly and naturally in the coupling method and the domain decomposition method of finite and boundary elements. Most of the material in this book has only appeared in the author's previous papers. Compared with its Chinese edition (Science Press, Beijing, 1993), many new research results such as the domain decomposition methods based on the natural boundary reduction are added.
Download or read book Integral Equations and Boundary Value Problems written by MD Raisinghania and published by S. Chand Publishing. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The tenth edition of Integral Equations and Boundary Value Problems continues to offer an in-depth presentation of integral equations for the solution of boundary value problems. The book provides a plethora of examples and step-by-step presentation of definitions, proofs of the standard results and theorems which enhance students' problem-solving skills. Solved examples and numerous problems with hints and answers have been carefully chosen, classified in various types and methods, and presented to illustrate the concepts discussed. With the author's vast experience of teaching mathematics, his approach of providing a one-stop solution to the students' problems is engaging which goes a long way for the reader to retain the knowledge gained.
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Download or read book Methods of Contour Integration written by M. L. Rasulov and published by Elsevier. This book was released on 2014-12-03 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Contour Integration contains two parts: (1) a systematic exposition of the computational method for solving boundary and mixed problems, and (2) the contour-integral method for investigating general linear mixed problems. The first part includes formulae for expanding arbitrary vector-valued functions in series from integral residues of solutions of boundary-value problems for systems of ordinary differential equations with discontinuous coefficients. These formulae give residue representations of solutions of the corresponding one-dimensional mixed problems for equations with discontinuous coefficients. The book also explains a computational method of separating the variables which is a generalization of the ordinary method of separating variables to the case of nonself-adjoint operators. In part two, the text discusses one-dimensional mixed problems for equations with discontinuous coefficients. Under regular boundary conditions, it proves the existence of solutions for these problems and the representability of the solutions in the form of contour integrals with a complex parameter. The text points out that the contour-integral method is also applicable to parabolic equations and to equations in which the coefficients are functions of time. The book is ideal for mathematicians, students, and professor of calculus and advanced mathematics.
Download or read book Partial Differential Equations and Boundary Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Download or read book Boundary Integral Methods written by Luigi Morino and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains edited papers from IABEM-90, the 1990 Symposium of the Interna tional Association for Boundary Element Methods (IABEM). As stated in the By-Laws of the Association, the purposes of IABEM are: 1. to promote the international exchange of technical information related to the devel opment and application of boundary-integral equation (BIE) formulations and their numerical implementation to problems in engineering and science, commonly referred to as the boundary element method (BEM); 2. to promote research and development activities for the advancement of boundary integral equation methods and boundary element solution algorithms; 3. to foster closer personal relationships within the BEM community of researchers. The objectives of the Symposium, in line with those of the Association, was to provide a forum where the two "souls" of the Association, i. e. , (i) mathematical foundations and numerical aspects, and (ii) engineering applications could be integrated. We believe that the first aspect has been neglected in too many of the BEM Symposia held in the past, which, with a few exceptions (notably, the IUTAM Symposia on the subject) have emphasized the practical aspects of the method. As a consequence, we have tried to give a stronger emphasis to the more theoretical issues: this is attested for instance, by the fact that the two general lectures were given by Prof. Gaetano Fichera, of the University of Rome "La Sapienza," and Prof.
Download or read book Numerical Boundary Value ODEs written by Ascher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to the workshop were in two formats. There were a small number of invited talks (ten of which are presented in this proceedings); the other contributions were in the rorm or poster sessions, for which there was no parallel activity in the workshop. We had attemptt'd to cover a number of topics and objectives in the talks. As a result, the general review papt'rs of O'Malley and Russell are intended to take a broader perspective, while the other papers are more specific. The contributions in this volume are divided (somewhat arbitrarily) into five groups. The first group concerns fundamental issues like conditioning and decoupling, which have only rect'ntly gained a proper appreciation of their centrality. Understanding of certain aspects or shooting methods ties in with these fundamental concepts. The papers of Russell, dt' Hoog and Mattheij all deal with these issues.
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Download or read book On the Kantorovich Treatment of Boundary Value Problems for Partial Differential Equations written by Arnold Noah Lowan and published by . This book was released on 1958 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Function Theoretic Solutions of Certain Boundary value Problems written by V. P. Sreedharan and published by . This book was released on 1961 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The domains of analyticity of solutions of the equation delta u! k square times u equals 0 in two independent variables are studied with a view to solving boundary-value problems in the large. The boundary value problems are transformed into function theoretic problems. Specifically the Sommerfeld half-plane problem for delta u! K square times u equals 0 is solved. A related result on integral equations is obtained. Green's functions for a wedge with various boundary conditions are constructed in the case of the equation delta u! k square times u equals 0. (Author).
Download or read book Direct and Indirect Boundary Integral Equation Methods written by Christian Constanda and published by CRC Press. This book was released on 2020-03-31 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering. Boundary integral equation methods (BIEM's) have certain advantages over other procedures for solving such problems: BIEM's are powerful, applicable to a wide variety of situations, elegant, and ideal for numerical treatment. Certain fundamental constructs in BIEM's are also essential ingredients in boundary element methods, often used by scientists and engineers. However, BIEM's are also sometimes more difficult to use in plane cases than in their three-dimensional counterparts. Consequently, the full, detailed BIEM treatment of two-dimensional problems has been largely neglected in the literature-even when it is more than marginally different from that applied to the corresponding three-dimensional versions. This volume discusses three typical cases where such differences are clear: the Laplace equation (one unknown function), plane strain (two unknown functions), and the bending of plates with transverse shear deformation (three unknown functions). The author considers each of these with Dirichlet, Neumann, and Robin boundary conditions. He subjects each to a thorough investigation-with respect to the existence and uniqueness of regular solutions-through several BIEM's. He proposes suitable generalizations of the concept of logarithmic capacity for plane strain and bending of plates, then uses these to identify contours where non-uniqueness may occur. In the final section, the author compares and contrasts the various solution representations, links them by means of boundary operators, and evaluates them for their suitability for
Download or read book Boundary Value Problems written by Fedor Dmitrievich Gakhov and published by . This book was released on 1966 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:
