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.
Download or read book Integral Equations and Their Applications written by Matiur Rahman and published by WIT Press. This book was released on 2007 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.
Download or read book Fractional Dispersive Models and Applications written by Panayotis G. Kevrekidis and published by Springer Nature. This book was released on with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Evolutionary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 2008-09-04 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
Download or read book Analytical and Numerical Methods for Volterra Equations written by Peter Linz and published by SIAM. This book was released on 1985-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Recent Advances in Partial Differential Equations Venice 1996 written by Peter D. Lax and published by American Mathematical Soc.. This book was released on 1998 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up solutions, conservation laws, Hamiltonian systems and others. The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. THe event allowed the international mathematics community to honor two of its outstanding members.
Download or read book Computation and Visualization of Geometric Partial Differential Equations written by Christopher Tiee and published by Lulu.com. This book was released on 2015-08-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an extended version of my PhD thesis which extends the theory of finite element exterior calculus (FEEC) to parabolic evolution equations. In the extended version, I explore some more precise visualizations of the defined quantities, as well as explain how the modern theory of functional analysis applies. In the main part, I extend the theory of approximating evolution equations in Euclidean space (using FEEC) to hypersurfaces. After these main results, I describe some possible extensions to nonlinear equations. A few appendices detail one of the original motivations for getting into this theory in the first place: canonical geometries given as steady state solutions and extremals of certain functionals.
Download or read book Extended Abstracts MWCAPDE 2023 written by Michael Ruzhansky and published by Springer Nature. This book was released on with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlocal Integral Equation Continuum Models written by Marta D'Elia and published by SIAM. This book was released on 2024-09-12 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well-known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. Nonlocal Integral Equation Continuum Models: Nonstandard Interaction Neighborhoods and Finite Element Discretizations is intended for mathematical and application researchers interested in alternatives to using partial differential equation models that better describe the phenomena they are interested in. The book will also be of use to computational scientists and engineers who need to make sense of how to use available software, improve existing software, or develop new software tailored to their application interests.
Download or read book Integral Methods in Low Frequency Electromagnetics written by Pavel Solin and published by John Wiley & Sons. This book was released on 2009-08-11 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern presentation of integral methods in low-frequency electromagnetics This book provides state-of-the-art knowledge on integral methods in low-frequency electromagnetics. Blending theory with numerous examples, it introduces key aspects of the integral methods used in engineering as a powerful alternative to PDE-based models. Readers will get complete coverage of: The electromagnetic field and its basic characteristics An overview of solution methods Solutions of electromagnetic fields by integral expressions Integral and integrodifferential methods Indirect solutions of electromagnetic fields by the boundary element method Integral equations in the solution of selected coupled problems Numerical methods for integral equations All computations presented in the book are done by means of the authors' own codes, and a significant amount of their own results is included. At the book's end, they also discuss novel integral techniques of a higher order of accuracy, which are representative of the future of this rapidly advancing field. Integral Methods in Low-Frequency Electromagnetics is of immense interest to members of the electrical engineering and applied mathematics communities, ranging from graduate students and PhD candidates to researchers in academia and practitioners in industry.
Download or read book Applications of Symmetry Methods to Partial Differential Equations written by George W. Bluman and published by Springer Science & Business Media. This book was released on 2009-10-30 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.
Download or read book Control Methods in PDE Dynamical Systems written by Fabio Ancona and published by American Mathematical Soc.. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperb These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. in addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. in all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.
Download or read book Evolution Equations Control Theory and Biomathematics written by Philippe Clement and published by CRC Press. This book was released on 1993-11-23 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the Third International Workshop Conference on Evolution Equations, Control Theory and Biomathematics, held in Hans-sur-Lesse, Belgium. The papers examine important advances in evolution equations related to physical, engineering and biological applications.
Download or read book Kernel Determination Problems in Hyperbolic Integro Differential Equations written by Durdimurod K. Durdiev and published by Springer Nature. This book was released on 2023-06-18 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional “impacts” or “explosions”. This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.
Download or read book Mesoscale Modeling in Chemical Engineering Part I written by and published by Academic Press. This book was released on 2015-11-26 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing Mesoscales of Multiscale Problems in Chemical Engineering, a volume in the Advances in Chemical Engineering series provides readers with the personal views of recognized authorities who present assessments of the state-of-the-art in the field and help readers develop an understanding of its further evolution. Subjects covered in the book are not limited to the classical chemical engineering disciplines. Contributions connecting chemical engineering to related scientific fields, either providing a fundamental basis or introducing new concepts and tools, are encouraged. This volume aims to create a balance between well developed areas such as process industry, transformation of materials, energy, and environmental issues, and areas where applications of chemical engineering are more recent or emerging. - Contains reviews by leading authorities in their respective areas - Provides up-to-date reviews of the latest techniques in the modeling of catalytic processes - Includes a broad mix of US and European authors, as well as academic/industrial/research institute perspectives - Provides discussions on the connections between computation and experimental methods
Download or read book Space Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
