Books in Partial differential equations

21-30 of 78 results in All results

Spectral Transform and Solitons

• 1st Edition
• Volume 13
• August 18, 2011
• F. Calogero + 1 more
• English
• eBook 978-0-08-087534-7

  9 7 8 - 0 - 0 8 - 0 8 7 5 3 4 - 7

Introduction to the Theory of Linear Partial Differential Equations

• 1st Edition
• Volume 14
• August 18, 2011
• J. Chazarain + 1 more
• English
• eBook 978-0-08-087535-4

  9 7 8 - 0 - 0 8 - 0 8 7 5 3 5 - 4

Second Order Linear Differential Equations in Banach Spaces

• 1st Edition
• Volume 108
• August 18, 2011
• H.O. Fattorini
• English
• eBook 978-0-08-087219-3

  9 7 8 - 0 - 0 8 - 0 8 7 2 1 9 - 3

Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

Transmutation Theory and Applications

• 1st Edition
• Volume 117
• August 18, 2011
• R. Carroll
• English
• eBook 978-0-08-087228-5

  9 7 8 - 0 - 0 8 - 0 8 7 2 2 8 - 5

Traveling Wave Analysis of Partial Differential Equations

• 1st Edition
• December 9, 2010
• Graham Griffiths + 1 more
• English
• Hardback 978-0-12-384652-5

  9 7 8 - 0 - 1 2 - 3 8 4 6 5 2 - 5
• eBook 978-0-12-384653-2

  9 7 8 - 0 - 1 2 - 3 8 4 6 5 3 - 2

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs.  The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

• 1st Edition
• Volume 213
• August 6, 2010
• Moysey Brio + 2 more
• English
• Hardback 978-0-12-133981-4

  9 7 8 - 0 - 1 2 - 1 3 3 9 8 1 - 4
• eBook 978-0-08-091704-7

  9 7 8 - 0 - 0 8 - 0 9 1 7 0 4 - 7

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc.The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them.In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes.

Introductory Differential Equations

• 3rd Edition
• September 9, 2009
• Martha L. Abell + 1 more
• English
• eBook 978-0-08-095845-3

  9 7 8 - 0 - 0 8 - 0 9 5 8 4 5 - 3

This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a "traditional" curriculum and takes the "traditional" (rather than "dynamical systems") approach. Introductory Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Note that some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries depending on the school, course, or instructor.

Boundary Value Problems

• 6th Edition
• July 24, 2009
• David L. Powers
• English
• Hardback 978-0-12-374719-8

  9 7 8 - 0 - 1 2 - 3 7 4 7 1 9 - 8
• eBook 978-0-08-088441-7

  9 7 8 - 0 - 0 8 - 0 8 8 4 4 1 - 7

Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods.The book contains nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises.Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems.

Mathematical Problems in Elasticity and Homogenization

• 1st Edition
• Volume 2
• June 15, 2009
• O.A. Oleinik + 2 more
• English
• eBook 978-0-08-087523-1

  9 7 8 - 0 - 0 8 - 0 8 7 5 2 3 - 1

This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof.It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

Handbook of Differential Equations: Evolutionary Equations

• 1st Edition
• Volume 5
• April 29, 2009
• C.M. Dafermos + 1 more
• English
• Hardback 978-0-444-53222-0

  9 7 8 - 0 - 4 4 4 - 5 3 2 2 2 - 0
• eBook 978-0-08-093259-0

  9 7 8 - 0 - 0 8 - 0 9 3 2 5 9 - 0

Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable