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Spherical And Plane Integral Operators For Pdes
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Book Synopsis Spherical and Plane Integral Operators for PDEs by : Karl K. Sabelfeld
Download or read book Spherical and Plane Integral Operators for PDEs written by Karl K. Sabelfeld and published by Walter de Gruyter. This book was released on 2013-10-29 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Stochastic Methods for Boundary Value Problems by : Karl K. Sabelfeld
Download or read book Stochastic Methods for Boundary Value Problems written by Karl K. Sabelfeld and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-09-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics. Contents: Introduction Random walk algorithms for solving integral equations Random walk-on-boundary algorithms for the Laplace equation Walk-on-boundary algorithms for the heat equation Spatial problems of elasticity Variants of the random walk on boundary for solving stationary potential problems Splitting and survival probabilities in random walk methods and applications A random WOS-based KMC method for electron–hole recombinations Monte Carlo methods for computing macromolecules properties and solving related problems Bibliography
Book Synopsis Mathematical Demoeconomy by : Yuri S. Popkov
Download or read book Mathematical Demoeconomy written by Yuri S. Popkov and published by Walter de Gruyter. This book was released on 2014-04-02 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aspires to lay the foundations of a new scientific discipline, demoeconomics, representing the synthesis of demography and spatial economics. This synthesis is performed in terms of interaction between population and its economic activity. The monograph appears a unique research work having no analogs in scientific literature. Demoeconomic systems are studied involving the macrosystems approach which combines the generalized entropy maximization principle and the local equilibria principle. Demoeconomic systems operate in an uncertain environment; thus and so, the monograph develops the methodology and technique of probabilistic modeling and forecasting of their evolution.
Book Synopsis Geometric Analysis of PDE and Several Complex Variables by : Francois Treves
Download or read book Geometric Analysis of PDE and Several Complex Variables written by Francois Treves and published by American Mathematical Soc.. This book was released on 2005 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
Book Synopsis Function Theoretic Methods in Partial Differential Equations by : Gilbert
Download or read book Function Theoretic Methods in Partial Differential Equations written by Gilbert and published by Academic Press. This book was released on 1969 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Function Theoretic Methods in Partial Differential Equations
Book Synopsis Global Analysis - Studies and Applications V by : Yuri G. Borisovich
Download or read book Global Analysis - Studies and Applications V written by Yuri G. Borisovich and published by Springer. This book was released on 2006-11-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume (a sequel to LNM 1108, 1214, 1334 and 1453) continues the presentation to English speaking readers of the Voronezh University press series on Global Analysis and Its Applications. The papers are selected fromtwo Russian issues entitled "Algebraic questions of Analysis and Topology" and "Nonlinear Operators in Global Analysis". CONTENTS: YuE. Gliklikh: Stochastic analysis, groups of diffeomorphisms and Lagrangian description of viscous incompressible fluid.- A.Ya. Helemskii: From topological homology: algebras with different properties of homological triviality.- V.V. Lychagin, L.V. Zil'bergleit: Duality in stable Spencer cohomologies.- O.R. Musin: On some problems of computational geometry and topology.- V.E. Nazaikinskii, B.Yu. Sternin, V.E.Shatalov: Introduction to Maslov's operational method (non-commutative analysis and differential equations).- Yu.B. Rudyak: The problem of realization of homology classes from Poincare up to the present.- V.G. Zvyagin, N.M. Ratiner: Oriented degree of Fredholm maps of non-negativeindex and its applications to global bifurcation of solutions.- A.A. Bolibruch: Fuchsian systems with reducible monodromy and the Riemann-Hilbert problem.- I.V. Bronstein, A.Ya. Kopanskii: Finitely smooth normal forms of vector fields in the vicinity of a rest point.- B.D. Gel'man: Generalized degree of multi-valued mappings.- G.N. Khimshiashvili: On Fredholmian aspects of linear transmission problems.- A.S. Mishchenko: Stationary solutions of nonlinear stochastic equations.- B.Yu. Sternin, V.E. Shatalov: Continuation of solutions to elliptic equations and localisation of singularities.- V.G. Zvyagin, V.T. Dmitrienko: Properness of nonlinear elliptic differential operators in H|lder spaces.
Book Synopsis Spherical and Plane Integral Operators for PDEs by : Karl K. Sabel'fel'd
Download or read book Spherical and Plane Integral Operators for PDEs written by Karl K. Sabel'fel'd and published by Walter de Gruyter. This book was released on 2013-10-29 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.
Book Synopsis Introduction to Partial Differential Equations with MATLAB by : Jeffery M. Cooper
Download or read book Introduction to Partial Differential Equations with MATLAB written by Jeffery M. Cooper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Numerical Solution of Ordinary and Partial Differential Equations by : L. Fox
Download or read book Numerical Solution of Ordinary and Partial Differential Equations written by L. Fox and published by Elsevier. This book was released on 2014-05-15 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solution of Ordinary and Partial Differential Equations is based on a summer school held in Oxford in August-September 1961. The book is organized into four parts. The first three cover the numerical solution of ordinary differential equations, integral equations, and partial differential equations of quasi-linear form. Most of the techniques are evaluated from the standpoints of accuracy, convergence, and stability (in the various senses of these terms) as well as ease of coding and convenience of machine computation. The last part, on practical problems, uses and develops the techniques for the treatment of problems of the greatest difficulty and complexity, which tax not only the best machines but also the best brains. This book was written for scientists who have problems to solve, and who want to know what methods exist, why and in what circumstances some are better than others, and how to adapt and develop techniques for new problems. The budding numerical analyst should also benefit from this book, and should find some topics for valuable research. The first three parts, in fact, could be used not only by practical men but also by students, though a preliminary elementary course would assist the reading.
Book Synopsis Integral Equation Methods for Evolutionary PDE by : Lehel Banjai
Download or read book Integral Equation Methods for Evolutionary PDE written by Lehel Banjai and published by Springer Nature. This book was released on 2022-11-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge–Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.
Book Synopsis An Introduction to Partial Differential Equations by : Yehuda Pinchover
Download or read book An Introduction to Partial Differential Equations written by Yehuda Pinchover and published by Cambridge University Press. This book was released on 2005-05-12 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students whilst extended solution sets are available to lecturers from [email protected].
Book Synopsis Commutative Harmonic Analysis III by : V.P. Havin
Download or read book Commutative Harmonic Analysis III written by V.P. Havin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at readers who have learned the principles of harmonic analysis, this book provides a variety of perspectives on this very important classical subject. The authors have written a truly outstanding book which distinguishes itself by its excellent expository style.
Book Synopsis Plane Waves and Spherical Means Applied to Partial Differential Equations by : Fritz John
Download or read book Plane Waves and Spherical Means Applied to Partial Differential Equations written by Fritz John and published by Courier Corporation. This book was released on 2004-07-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results follow from those identities. 1955 edition.
Book Synopsis Fourier Integrals in Classical Analysis by : Christopher D. Sogge
Download or read book Fourier Integrals in Classical Analysis written by Christopher D. Sogge and published by Cambridge University Press. This book was released on 2017-04-27 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.
Book Synopsis Inverse Problems in Partial Differential Equations by : David L. Colton
Download or read book Inverse Problems in Partial Differential Equations written by David L. Colton and published by SIAM. This book was released on 1990-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
