Perturbation Methods for Engineers and ScientistsPerturbation Methods for Engineers and Scientists



These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions.

Author: AlanW. Bush

Publisher: Routledge

ISBN: 9781351425353

Category:

Page: 320

View: 244

The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.

Perturbation Methods for Engineers and ScientistsPerturbation Methods for Engineers and Scientists



C.M. and Onzag, SA , Advanced Mathematical Methods for Scientists and Engineers, McGrawHill. New York, 1978. Cole, J.D., Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, MA, 1968. Copaon, E.T, Asymptotic Expansions, ...

Author: AlanW. Bush

Publisher: Routledge

ISBN: 9781351425360

Category:

Page: 320

View: 390

The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.

Perturbation Methods for Engineers and ScientistsPerturbation Methods for Engineers and Scientists



This text provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions.

Author: Alan W. Bush

Publisher: CRC-Press

ISBN: 0849386144

Category:

Page: 320

View: 941

This text provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Computer programs are included to enable students to explore particular ideas, as well as realistic case studies of industrial applications.

Perturbation Methods in Science and EngineeringPerturbation Methods in Science and Engineering



Perturbation methods for engineers and scientists. Boca Raton, FL: CRC Press. Celia, C. W., Nice, A. T. F., & Elliott, K. F. (1991). Advanced mathematics, 3. London, GB: Macmillan. Cole, J. D. (1968). Perturbation methods in applied ...

Author: Reza N. Jazar

Publisher: Springer Nature

ISBN: 9783030734626

Category:

Page: 578

View: 210

Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems. Illustrates all key concepts with solved examples; Includes numerous exercises for each chapter; Covers both time and steady state responses of nonlinear differential equations; Covers necessary theory and applied to a variety of topics in optimization and control.

The Stochastic Perturbation Method for Computational MechanicsThe Stochastic Perturbation Method for Computational Mechanics



(1992) Numerical Methods for Engineers and Scientists, McGraw-Hill, New York. [48] Honda, R. (2005) Stochastic BEM with spectral approach in elastostatic and elastodynamic problems with geometrical uncertainty. Engineering Analysis with ...

Author: Marcin Kaminski

Publisher: John Wiley & Sons

ISBN: 9781118481837

Category:

Page: 352

View: 527

Probabilistic analysis is increasing in popularity and importance within engineering and the applied sciences. However, the stochastic perturbation technique is a fairly recent development and therefore remains as yet unknown to many students, researchers and engineers. Fields in which the methodology can be applied are widespread, including various branches of engineering, heat transfer and statistical mechanics, reliability assessment and also financial investments or economical prognosis in analytical and computational contexts. Stochastic Perturbation Method in Applied Sciences and Engineering is devoted to the theoretical aspects and computational implementation of the generalized stochastic perturbation technique. It is based on any order Taylor expansions of random variables and enables for determination of up to fourth order probabilistic moments and characteristics of the physical system response. Key features: Provides a grounding in the basic elements of statistics and probability and reliability engineering Describes the Stochastic Finite, Boundary Element and Finite Difference Methods, formulated according to the perturbation method Demonstrates dual computational implementation of the perturbation method with the use of Direct Differentiation Method and the Response Function Method Accompanied by a website (www.wiley.com/go/kaminski) with supporting stochastic numerical software Covers the computational implementation of the homogenization method for periodic composites with random and stochastic material properties Features case studies, numerical examples and practical applications Stochastic Perturbation Method in Applied Sciences and Engineering is a comprehensive reference for researchers and engineers, and is an ideal introduction to the subject for postgraduate and graduate students.

Fuzzy Differential Equations and Applications for Engineers and ScientistsFuzzy Differential Equations and Applications for Engineers and Scientists



Abdulaziz O, Hashim I, Momani S. (2008) Application of homotopy-perturbation method to fractional IVPs. J Comput Appl Math 216:574–584. Balci MA, Yildirim A. (2011) Analysis of fractional nonlinear differential equations using the ...

Author: S. Chakraverty

Publisher: CRC Press

ISBN: 9781315355535

Category:

Page: 224

View: 446

Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work?provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.

Mathematical Tools for PhysicistsMathematical Tools for Physicists



Jones, C.K.R.T. (1994) Geometric singular perturbation theory, in Dynamical Systems (Montecatini Terme, 1994), ... Bender, C.M. and Orszag, S.A. (1999) Advanced Mathematical Methods for Scientists and Engineers, Springer-Verlag, ...

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 9783527411887

Category:

Page: 632

View: 612

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Beyond PerturbationBeyond Perturbation



[1] Cole, J.D. Perturbation Methods in Applied Mathematics. Blaisdell Publishing Company, Waltham, ... [2] Von Dyke, M. Perturbation Methods in Fluid Mechanics. ... [9] Bush, A.W. Perturbation Methods For Engineers and Scientists.

Author: Shijun Liao

Publisher: CRC Press

ISBN: 9780203491164

Category:

Page: 336

View: 419

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for

Perturbation Methods with Applications in Science and EngineeringPerturbation Methods with Applications in Science and Engineering



Introduction to Perturbation Techniques. New York: A Wiley-Interscience publication; 1981 [27] Settari A, Aziz K. A computer model for two-phase coning saturation. Society of Petroleum Engineers Journal. 1974;14(3):221-236 [28] Peres ...

Author: İlkay Bakırtaş

Publisher: BoD – Books on Demand

ISBN: 9781789842555

Category:

Page: 168

View: 530

The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.

Handbook of Mathematics for Engineers and ScientistsHandbook of Mathematics for Engineers and Scientists



Kevorkian, J. and Cole, J. D., Multiple Scale and Singular Perturbation Methods, Springer-Verlag, New York, 1996. Korn, G. A. and Korn, T. M., Mathematical Handbook for Scientists and Engineers, 2nd Edition, Dover Publications, ...

Author: Andrei D. Polyanin

Publisher: CRC Press

ISBN: 9781420010510

Category:

Page: 1544

View: 438

The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible. Organized in ascending order of complexity, the material is divided into two parts. The first part is a coherent survey of the most important definitions, formulas, equations, methods, and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including those of exact solutions of various types of equations. This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.