Collocation Methods for Volterra Integral and Related Functional Differential Equations

Author: Hermann Brunner

Publisher: Cambridge University Press

ISBN: 9780521806152

Category: Mathematics

Page: 597

View: 8364

Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.

The Classical Theory of Integral Equations

A Concise Treatment

Author: Stephen M. Zemyan

Publisher: Springer Science & Business Media

ISBN: 0817683496

Category: Mathematics

Page: 344

View: 4930

The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.

Numerical Solution of Ordinary Differential Equations

Author: Kendall Atkinson,Weimin Han,David E. Stewart

Publisher: John Wiley & Sons

ISBN: 1118164520

Category: Mathematics

Page: 272

View: 1485

A concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures a coherent and accessible discussion of key topics, including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to test and build their knowledge of the presented methods, and a related Web site features MATLAB® programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics. Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.

Numerical Solution of Elliptic Problems

Author: Garrett Birkhoff,Robert E. Lynch

Publisher: SIAM

ISBN: 9781611970869

Category: Boundary value problems

Page: 319

View: 1713

A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.

Contact Problems in Elasticity

A Study of Variational Inequalities and Finite Element Methods

Author: N. Kikuchi,J. T. Oden

Publisher: SIAM

ISBN: 9781611970845

Category: Collisions (Physics)

Page: 495

View: 2058

The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

Methods and Applications of Interval Analysis

Author: Ramon E. Moore

Publisher: SIAM

ISBN: 9781611970906

Category: Interval analysis (Mathematics)

Page: 190

View: 1693

This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing.


Author: N.A

Publisher: N.A


Category: Mechanical engineering

Page: N.A

View: 5912


Winter Annual Meeting

Technical papers presented and available

Author: American Society of Mechanical Engineers

Publisher: N.A


Category: Mechanical engineering

Page: N.A

View: 3416


Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1490108580

Category: Science

Page: 1215

View: 8502

Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Applied Analysis. The editors have built Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Analysis in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied, Analytical, and Imaging Sciences Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at

Handbook of Integral Equations

Second Edition

Author: Andrei D. Polyanin,Alexander V. Manzhirov

Publisher: CRC Press

ISBN: 1135436126

Category: Mathematics

Page: 1144

View: 3043

Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, Wiener–Hopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. With 300 additional pages, this edition covers much more material than its predecessor. New to the Second Edition • New material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions • More than 400 new equations with exact solutions • New chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs • Additional examples for illustrative purposes To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity. The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations.

Viscoelasticity and Rheology

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 16–18, 1984

Author: Arthur S. Lodge,Michael Renardy,John A. Nohel

Publisher: Academic Press

ISBN: 1483263355

Category: Technology & Engineering

Page: 456

View: 6111

Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation. This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws. This book will prove useful to chemical engineers, researchers, and students.

Applied and Industrial Mathematics in Italy III

Author: Enrico De Bernardis

Publisher: World Scientific

ISBN: 9814280305

Category: Electronic books

Page: 575

View: 2056

This book provides an up-to-date overview of research articles in applied and industrial mathematics in Italy. This is done through the presentation of a number of investigations focusing on subjects as nonlinear optimization, life science, semiconductor industry, cultural heritage, scientific computing and others. This volume is important as it gives a report on modern applied and industrial mathematics, and will be of specific interest to the community of applied mathematicians. This book collects selected papers presented at the 9th Conference of SIMAI. The subjects discussed include image analysis methods, optimization problems, mathematics in the life sciences, differential models in applied mathematics, inverse problems, complex systems, innovative numerical methods and others. Sample Chapter(s). Chapter 1: Multichannel Wavelet Scheme for Color Image Processing (759 KB). Contents: Existence and Uniqueness for a Three Dimensional Model of Ferromagnetism (V Berti et al.); Wave Propagation in Continuously-Layered Electromagnetic Media (G Caviglia & A Morro); Mathematical Models for Biofilms on the Surface of Monuments (F Clarelli et al.); Conservation Laws with Unilateral Constraints in Traffic Modeling (R M Colombo et al.); On a Model for the Codiffusion of Isotopes (E Comparini et al.); Multiscale Models of Drug Delivery by Thin Implantable Devices (C D''Angelo & P Zunino); A Mathematical Model of Duchenne Muscular Dystrophy (G Dell''Acqua & F Castiglione); A Dissipative System Arising in Strain-Gradient Plasticity (L Giacomelli & G Tomassetti); Material Symmetry and Invariants for a 2D Fiber-Reinforced Network with Bending Stiffness (G Indelicato); Kinetic Treatment of Charge Carrier and Phonon Transport in Graphene (P Lichtenberger et al.); Mathematical Models and Numerical Simulation of Controlled Drug Release (S Minisini & L Formaggia); A Lattice Boltzmann Model on Unstructured Grids with Application in Hemodynamics (G Pontrelli et al.); Toward Analytical Contour Dynamics (G Riccardi & D Durante); Thermo-Mechanical Modeling of Ground Deformation in Volcanic Areas (D Scandura et al.); and other papers. Readership: Researchers in applied and computational mathematics.

Numerical Approximation Methods

π ≈ 355/113

Author: Harold Cohen

Publisher: Springer Science & Business Media

ISBN: 1441998373

Category: Mathematics

Page: 485

View: 3908

This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.

Theory and Applications of Fractional Differential Equations

Author: Anatoliĭ Aleksandrovich Kilbas,H. M. Srivastava,Juan J. Trujillo

Publisher: Elsevier

ISBN: 9780444518323

Category: Mathematics

Page: 523

View: 3470

This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.