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Author : T.Y. Na
Publisher : Academic Press
Page : 321 pages
File Size : 46,6 Mb
Release : 1980-01-18
Category : Computers
ISBN : 9780080956534
Computational Methods in Engineering Boundary Value Problems
Author : S. P. Venkateshan,Prasanna Swaminathan
Publisher : Springer Nature
Page : 824 pages
File Size : 52,8 Mb
Release : 2023-05-31
Category : Technology & Engineering
ISBN : 9783031082269
The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial value problems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.
Author : Ali Ümit Keskin
Publisher : Springer
Page : 517 pages
File Size : 46,8 Mb
Release : 2019-06-19
Category : Technology & Engineering
ISBN : 9783030210809
This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).
Author : Grant B. Gustafson,Calvin H. Wilcox
Publisher : Springer Science & Business Media
Page : 754 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461206330
This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations. Destined to become the definitive work in the field, the book uses a practical engineering approach based upon solving equations and incorporates computational techniques throughout.
Author : Ralph E. White,Venkat R. Subramanian
Publisher : Springer Science & Business Media
Page : 871 pages
File Size : 54,5 Mb
Release : 2010-02-06
Category : Science
ISBN : 9783642043116
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.
Author : Kumar Nandakumar,Robert Hayes,Joseph Mmbaga
Publisher : Na
Page : 426 pages
File Size : 43,9 Mb
Release : 2021-01-09
Category : Mathematics
ISBN : 1989024068
Revolutionary advances in hardware and software technology have made computer aided design and analysis a standard tool in engineering practice. While this puts a lot of power at the hands of the end user, in order to use them wisely and interpret the results correctly, the users are expected to have a sound knowledge of the relationship between the physical world and the mathematical model and that between the mathematical model and the numerical approximation. The text examines the link between the mathematical and the numerical model in a succinct manner. Numerical algorithms relevant to engineers are developed and applied to solve industrial problems.The text is intended for senior level undergraduate and first year graduate students without rigorous training in numerical analysis. The following topics are covered both in theory and practical examples.-Roots of non-linear equations.-Systems of linear algebraic equations.-Interpolation and curve fitting.-Numerical differentiation and integration.-Ordinary differential equation - initial value problems.-Ordinary differential equations - boundary value problems.-Partial differential equations.
Author : John R. Hauser
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 47,5 Mb
Release : 2009-03-24
Category : Technology & Engineering
ISBN : 9781402099205
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Author : Ivar Stakgold,Michael J. Holst
Publisher : John Wiley & Sons
Page : 883 pages
File Size : 46,6 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9780470906521
Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
Author : M.K. Jain
Publisher : New Age International
Page : 848 pages
File Size : 42,8 Mb
Release : 2003
Category : Electronic
ISBN : 8122414613
Author : Kenneth J. Beers
Publisher : Cambridge University Press
Page : 496 pages
File Size : 50,5 Mb
Release : 2007
Category : Computers
ISBN : 0521859719
Applications of numerical mathematics and scientific computing to chemical engineering.
Author : Mohamed Zerroukat,Chris R. Chatwin
Publisher : Research Studies PressLtd
Page : 212 pages
File Size : 45,8 Mb
Release : 1994
Category : Technology & Engineering
ISBN : 0863801684
This book reviews and compares some well-known numerical methods and more recent contributions for solving both moving boundary and boundary value problems. Recent advances in the finite difference solution of linear and non-linear partial differential equations are also presented and algorithmic manipulations which enhance the computational efficiency are incorporated into the overall schemes.
Author : Paul Farrell,Alan Hegarty,John M. Miller,Eugene O'Riordan,Grigory I. Shishkin
Publisher : CRC Press
Page : 256 pages
File Size : 45,8 Mb
Release : 2000-03-30
Category : Computers
ISBN : 9781482285727
Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They pres
Author : Simon Sirca,Martin Horvat
Publisher : Springer Science & Business Media
Page : 724 pages
File Size : 44,9 Mb
Release : 2012-12-17
Category : Science
ISBN : 9783642324789
This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.
Author : J.N. Reddy
Publisher : CRC Press
Page : 595 pages
File Size : 41,9 Mb
Release : 2024-03-19
Category : Mathematics
ISBN : 9781003836087
Computational Methods in Engineering: Finite Difference, Finite Volume, Finite Element, and Dual Mesh Control Domain Methods provides readers with the information necessary to choose appropriate numerical methods to solve a variety of engineering problems. Explaining common numerical methods in an accessible yet rigorous manner, the book details the finite element method (FEM), finite volume method (FVM) and importantly, a new numerical approach, dual mesh control domain method (DMCDM). Numerical methods are crucial to everyday engineering. The book begins by introducing the various methods and their applications, with example problems from a range of engineering disciplines including heat transfer, solid and structural mechanics, and fluid mechanics. It highlights the strengths of FEM, with its systematic procedure and modular steps, and then goes on to explain the uses of FVM. It explains how DMCDM embodies useful parts of both FEM and FVM, particularly in its use of the control domain method and how it can provide a comprehensive computational approach. The final chapters look at ways to use different numerical methods, primarily FEM and DMCDM, to solve typical problems of bending of beams, axisymmetric circular plates, and other nonlinear problems. This book is a useful guide to numerical methods for professionals and students in all areas of engineering and engineering mathematics.
Author : Karan S. Surana
Publisher : CRC Press
Page : 256 pages
File Size : 50,6 Mb
Release : 2018-10-31
Category : Mathematics
ISBN : 9780429647864
Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors