Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, ...

Author: James P Howard, II

Publisher: CRC Press

ISBN: 9781351646505

Category: Mathematics

Page: 257

View: 356

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

This book was written for a senior undergraduate or a first year graduate student course in chemical engineering. Most of the examples in this book were done in Maple 10. However, the codes should run in the most recent version of Maple.

Author: Ralph E. White

Publisher: Springer Science & Business Media

ISBN: 3642043119

Category: Science

Page: 860

View: 429

This book presents Maple solutions to a wide range of problems relevant to chemical engineers and others. Many of these solutions use Maple’s symbolic capability to help bridge the gap between analytical and numerical solutions. The readers are strongly encouraged to refer to the references included in the book for a better understanding of the physics involved, and for the mathematical analysis. This book was written for a senior undergraduate or a first year graduate student course in chemical engineering. Most of the examples in this book were done in Maple 10. However, the codes should run in the most recent version of Maple. We strongly encourage the readers to use the classic worksheet (*. mws) option in Maple as we believe it is more user-friendly and robust. In chapter one you will find an introduction to Maple which includes simple basics as a convenience for the reader such as plotting, solving linear and nonlinear equations, Laplace transformations, matrix operations, ‘do loop,’ and ‘while loop. ’ Chapter two presents linear ordinary differential equations in section 1 to include homogeneous and nonhomogeneous ODEs, solving systems of ODEs using the matrix exponential and Laplace transform method. In section two of chapter two, nonlinear ordinary differential equations are presented and include simultaneous series reactions, solving nonlinear ODEs with Maple’s ‘dsolve’ command, stop conditions, differential algebraic equations, and steady state solutions. Chapter three addresses boundary value problems.

This book presents numerical methods and computational aspects for linear integral equations.

Author: Prem Kythe

Publisher: Springer Science & Business Media

ISBN: 0817641920

Category: Mathematics

Page: 508

View: 937

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

From geometric integration and its applications, and linear programming and condition numbers under the real number computational model, to chaos in finite difference schemes, these essays explore the foundational issues of computational mathematics.

Petcu, M., Temam, R., Ziane, M. (2008). Mathematical problems for the primitive
equations with viscosity. In: Ciarlet, P.G. (eds.), Handbook of Numerical Analysis.
Special Issue on Some Mathematical Problems in Geophysical Fluid Dynamics ...

Author:

Publisher: Elsevier

ISBN: 0080931030

Category: Computers

Page: 784

View: 107

This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered. • Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics • Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences • Contributions uniquely address central problems and provide a survey of the frontier of research

This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.

Author: Philippe G. Ciarlet

Publisher: Elsevier

ISBN: 9780444530479

Category: Mathematics

Page: 801

View: 374

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.

Error Estimation and Adaptive Discretization Methods in Computational Fluid
Dynamics. M. Griebel, M. A. Schweitzer ... B. N. Khoromskij, G. Wittum, Numerical
Solution of Elliptic Dijferential Equations by Reduction to the Interface. A. Iske ... R. Kornhuber, R. Hoppe, J .Périaux, O. Pironneau, O. Wildlund, J. Xu (eds.),
Domain ...

Author: Martin Peters

Publisher: Springer Science & Business Media

ISBN: 9783642044663

Category: Computers

Page: 134

View: 179

All over the world sport plays a prominent role in society: as a leisure activity for many, as an ingredient of culture, as a business and as a matter of national prestige in such major events as the World Cup in soccer or the Olympic Games. Hence, it is not surprising that science has entered the realm of sports, and, in particular, that computer simulation has become highly relevant in recent years. This is explored in this book by choosing five different sports as examples, demonstrating that computational science and engineering (CSE) can make essential contributions to research on sports topics on both the fundamental level and, eventually, by supporting athletes’ performance.

This volume presents an introduction to the three numerical methods most commonly used in the mechanical analysis of deformable solids, viz. the finite element method (FEM), the linear iteration method (LIM), and the finite difference ...

Author: A. Curnier

Publisher: Springer Science & Business Media

ISBN: 9789401111126

Category: Technology & Engineering

Page: 404

View: 873

This volume presents an introduction to the three numerical methods most commonly used in the mechanical analysis of deformable solids, viz. the finite element method (FEM), the linear iteration method (LIM), and the finite difference method (FDM). The book has been written from the point of view of simplicity and unity; its originality lies in the comparable emphasis given to the spatial, temporal and nonlinear dimensions of problem solving. This leads to a neat global algorithm. Chapter 1 addresses the problem of a one-dimensional bar, with emphasis being given to the virtual work principle. Chapters 2--4 present the three numerical methods. Although the discussion relates to a one-dimensional model, the formalism used is extendable to two-dimensional situations. Chapter 5 is devoted to a detailed discussion of the compact combination of the three methods, and contains several sections concerning their computer implementation. Finally, Chapter 6 gives a generalization to two and three dimensions of both the mechanical and numerical aspects. For graduate students and researchers whose work involves the theory and application of computational solid mechanics.

This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years.

Author: Adhemar Bultheel

Publisher: World Scientific

ISBN: 9789812836267

Category: Electronic books

Page: 240

View: 302

The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

Author: Azmy S. Ackleh

Publisher: CRC Press

ISBN: 1420091581

Category: Mathematics

Page: 628

View: 413

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.

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 ...

Author: C. Brezinski

Publisher: Gulf Professional Publishing

ISBN: 0444506179

Category: Mathematics

Page: 505

View: 536

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.

Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike. This volume offers investigations.

Author:

Publisher: Elsevier

ISBN: 9780080932026

Category: Mathematics

Page: 824

View: 392

Non-Newtonian flows and their numerical simulations have generated an abundant literature, as well as many publications and references to which can be found in this volume’s articles. This abundance of publications can be explained by the fact that non-Newtonian fluids occur in many real life situations: the food industry, oil & gas industry, chemical, civil and mechanical engineering, the bio-Sciences, to name just a few. Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike. This volume offers investigations. Results and conclusions that will no doubt be useful to engineers and computational and applied mathematicians who are focused on various aspects of non-Newtonian Fluid Mechanics. New review of well-known computational methods for the simulation viscoelastic and viscoplastic types.; Discusses new numerical methods that have proven to be more efficient and more accurate than traditional methods.; Articles that discuss the numerical simulation of particulate flow for viscoelastic fluids.;

On the occasion of this new edition, the text was enlarged by several new sections.

Author: J. Stoer

Publisher: Springer Science & Business Media

ISBN: 9781475722727

Category: Mathematics

Page: 660

View: 916

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

Error Estimation and Adaptive Discretization Methods in Computational Fluid
Dynamics. M. Griebel, M.A. Schweitzer ... B.N. Khoromskij, G. Wittum, Numerical
Solution of Elliptic Differential Equations by Reduction to the Interface. A. Iske ... R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Wildlund, J.Xu (eds.),
Domain ...

Author: Björn Engquist

Publisher: Springer Science & Business Media

ISBN: 9783642219436

Category: Computers

Page: 430

View: 876

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

[1] [2] [3] [4] [7] [8] [9] [10] [11] [12] [13] [14] Phillips, R., Armstrong, R., Brown, R.,
Graham, A., & Abbott, J., Numerical analysis of normal stress in non-Newtonian
boundary layer flow. Physics of Fluids A, 4(1), pp. 30–40, 1992. Buyevich, I.

Author: A.A. Mammoli

Publisher: WIT Press

ISBN: 9781845640798

Category: Computers

Page: 416

View: 579

Fluid Dynamics is one of the most important topics of applied mathematics and physics. Together with complex flows and turbulence, multiphase flows remains one of the most challenging areas of computational mechanics, and even seemingly simple problems remain unsolved to date. Multiphase flows are found in all areas of technology, at all length scales and flow regimes. The fluids involved can be compressible or incompressible, linear or nonlinear. Because of the complexity of the problem, it is often essential to utilize advanced computational and experimental methods to solve the complex equations that describe them. Challenges in these simulations include nonlinear fluids, treating drop breakup and coalescence, characterizing phase structures, and many others.This volume brings together work presented at the Fourth International Conference on Computational and Experimental Methods in Multiphase and Complex Flows. Featured topics include: Suspensions; Bubble and Drop Dynamics; Flow in Porous Media; Interfaces; Turbulent Flow; Injectors and Nozzles; Particle Image Velocimetry; Macroscale Constitutive Models; Large Eddy Simulation; Finite Volumes; Interface Tracking Methods; Biological Flows; Environmental Multiphase Flow; Phase Changes and Stochastic Modelling.

[2] Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for
Electromagnetics, New York: IEEE Press, 2001. [3] Itoh, T., (ed.), Numerical
Techniques for Microwave and Millimeter-Wave Passive Structures, New York:
Wiley, 1989, ...

Author: Ramesh Garg

Publisher: Artech House

ISBN: 9781596933866

Category: Electromagnetic waves

Page: 528

View: 138

Achieve optimal microwave system performance by mastering the principles and methods underlying today's powerful computational tools and commercial software in electromagnetics. This authoritative resource offers you clear and complete explanation of this essential electromagnetics knowledge, providing you with the analytical background you need to understand such key approaches as MoM (method of moments), FDTD (Finite Difference Time Domain) and FEM (Finite Element Method), and Green's functions. This comprehensive book includes all math necessary to master the material. Moreover, it features numerous solved problems that help ensure your understanding of key concepts throughout the book.

Error Estimation and Adaptive Discretization Methods in Computational Fluid
Dynamics. M. Griebel, M.A. Schweitzer ... B.N. Khoromskij, G. Wittum, Numerical
Solution of Elliptic Differential Equations by Reduction to the Interface. A. Iske ... R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Wildlund, J.Xu (eds.),
Domain ...

Author: Ivan G. Graham

Publisher: Springer Science & Business Media

ISBN: 9783642220616

Category: Mathematics

Page: 374

View: 466

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

The aim of this book is to facilitate the sharing of ideas, problems and methodologies between computational scientists and engineers in several disciplines.

Author: T. E. Simos

Publisher: World Scientific

ISBN: 9812704655

Category: Mathematics

Page: 716

View: 859

In the past few decades, many significant insights have been gained into several areas of computational methods in sciences and engineering. New problems and methodologies have appeared in some areas of sciences and engineering. There is always a need in these fields for the advancement of information exchange. The aim of this book is to facilitate the sharing of ideas, problems and methodologies between computational scientists and engineers in several disciplines. Extended abstracts of papers on the recent advances regarding computational methods in sciences and engineering are provided. The book briefly describes new methods in numerical analysis, computational mathematics, computational and theoretical physics, computational and theoretical chemistry, computational biology, computational mechanics, computational engineering, computational medicine, high performance computing, etc.

This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large ...

Author: Andreas Hohmann

Publisher: Springer Science & Business Media

ISBN: 0387954104

Category: Mathematics

Page: 340

View: 170

This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large systems and numerical integrations. The presentation draws on geometrical intuition wherever appropriate and is supported by a large number of illustrations, exercises, and examples.