Classical and Modern Numerical Analysis

Theory, Methods and Practice

Author: Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer

Publisher: CRC Press

ISBN: 9781420091588

Category: Mathematics

Page: 628

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Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

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: 1960

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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 Analysis: Historical Developments in the 20th Century

Author: C. Brezinski,L. Wuytack

Publisher: Gulf Professional Publishing

ISBN: 9780444506177

Category: Mathematics

Page: 505

View: 6931

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Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

The State of the art in numerical analysis

based on the proceedings of a joint IMA/SIAM conference on the state of the art in numerical analysis held in Cambridge in April 1986

Author: A. Iserles,Michael James David Powell,Institute of Mathematics and Its Applications,Society for Industrial and Applied Mathematics

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 719

View: 8061

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Very Good,No Highlights or Markup,all pages are intact.

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: 4960

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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.

The numerical solution of Volterra equations

Author: Hermann Brunner,Pieter Jacobus Houwen

Publisher: Elsevier Science Ltd

ISBN: 9780444700735

Category: Mathematics

Page: 588

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This monograph presents the theory and modern numerical analysis of Volterra integral and integro-differential equations, including equations with weakly singular kernels. While the research worker will find an up-to-date account of recent developments of numerical methods for such equations, including an extensive bibliography, the authors have tried to make the book accessible to the non-specialist possessing only a limited knowledge of numerical analysis. After an introduction to the theory of Volterra equations and to numerical integration, the book covers linear methods and Runge-Kutta methods, collocation methods based on polynomial spline functions, stability of numerical methods, and it surveys computer programs for Volterra integral and integro-differential equations.

A First Course in Integral Equations

Author: Abdul-Majid Wazwaz

Publisher: World Scientific

ISBN: 9789810231019

Category: Mathematics

Page: 208

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This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis.

Applied and Industrial Mathematics in Italy III

Author: Enrico De Bernardis

Publisher: World Scientific

ISBN: 9814280305

Category: Electronic books

Page: 575

View: 1055

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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: 5197

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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.

Recent Advances in Numerical Methods and Applications II

Author: Oleg P Iliev,Mikhail S Kaschiev,Svetozar D Margenov,Blagovest H Sendov,Panayot S Vassilevski

Publisher: World Scientific

ISBN: 9814531855

Category:

Page: 924

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This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications. Contents: Computational Issues in Large Scale Eigenvalue ProblemsCombustion Modeling in Industrial FurnacesMonte Carlo MethodsMultilevel Methods for Incompressible Viscous FlowsApproximation of Nonlinear and Functional PDEsSolving Linear Systems with Error ControlRegular Numerical Methods for Inverse and Ill-Posed ProblemsMultifield ProblemsParallel and Distributed Numerical Computing with ApplicationsParameter-Robust Numerical Methods for Singularly Perturbed and Convection-Dominated ProblemsFinite Difference MethodsFinite Element MethodsFinite Volume MethodsBoundary Element MethodsNumerical Linear AlgebraNumerical Methods for Nonlinear ProblemsNumerical Methods for Multiscale ProblemsMultigrid and Domain DecompositionComputational Fluid DynamicsMathematical Modelling in Structural MechanicsEnvironmental ModellingEngineering Applications Readership: Researchers in applied mathematics and computational physics. Keywords:Numerical Methods and Applications;General Finite Difference;General Numerical Linear Algebra;Parallel Computations;Nonlinear Problems and Multiscale Methods

Differential Equations and Nonlinear Mechanics

Author: K. Vajravelu

Publisher: Springer Science & Business Media

ISBN: 9780792368670

Category: Mathematics

Page: 435

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The book includes chapters written by well-known mathematicians and engineers. The topics include nonlinear differential equations, nonlinear dynamics, neural networks, modeling and dissipative processes, nonlinear ODE, nonlinear PDE, nonlinear mechanics, and fuzzy differential equations. The chapters are self-contained and contain new results. The book is suitable for anyone interested in pursuing research in the fields mentioned above.

Recent Advances in Scientific Computing and Applications

Author: Jichun Li,Hongtao Yang,Eric Alexander Machorro

Publisher: American Mathematical Soc.

ISBN: 0821887378

Category: Mathematics

Page: 382

View: 9368

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This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.

Topics in numerical analysis

proceedings of the S.E.R.C. Summer School, Lancaster, July 19-August 21, 1981

Author: Peter R. Turner

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 202

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Integral Equations

Theory and Numerical Treatment

Author: Wolfgang Hackbusch

Publisher: Springer Science & Business Media

ISBN: 9783764328719

Category: Mathematics

Page: 362

View: 998

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The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.