Fitted Numerical Methods for Singular Perturbation Problems

Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to b

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence

This book on singular perturbation problems - in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour - is devoted to the construction and analysis of numerical met

This book presents an introduction to singular-perturbation problems, problems which depend on a parameter in such a way that solutions behave non-uniformly as the parameter tends toward some limiting value of interest. The author considers and solves a variety of problems, mostly for ordinary differential equations. He constructs (approximate) solutions for oscillation problems, using the methods of averaging and of multiple scales. For problems of the nonoscillatory type, where solutions exhibit 'fast dynamics' in a thin initial layer, he derives solutions using the O'Malley/Hoppensteadt method and the method of matched expansions. He obtains solutions for boundary-value problems, where solutions exhibit rapid variation in thin layers, using a multivariable method. After a suitable approximate solution is constructed, the author linearizes the problem about the proposed approximate solution, and, emphasizing the use of the Banach/Picard fixed-point theorem, presents a study of the li

Perturbation methods are one of the fundamental tools used by all applied mathematicians and theoretical physicists. In this book, the author has managed to present the theory and techniques underlying such methods in a manner which will give the text wide appeal to students from a broad range of disciplines. Asymptotic expansions, strained coordinates and multiple scales are illustrated by copious use of examples drawn from all areas of applied mathematics and theoretical physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather to give a physical understanding of the subtle balances in a complex problem.

This book presents an introduction to singular-perturbation problems, problems which depend on a parameter in such a way that solutions behave non-uniformly as the parameter tends toward some limiting value of interest. The author considers and solves a variety of problems, mostly for ordinary differential equations. He constructs (approximate) solutions for oscillation problems, using the methods of averaging and of multiple scales. For problems of the nonoscillatory type, where solutions exhibit 'fast dynamics' in a thin initial layer, he derives solutions using the O'Malley/Hoppensteadt method and the method of matched expansions. He obtains solutions for boundary-value problems, where solutions exhibit rapid variation in thin layers, using a multivariable method. After a suitable approximate solution is constructed, the author linearizes the problem about the proposed approximate solution, and, emphasizing the use of the Banach/Picard fixed-point theorem, presents a study of the li

Featuring international contributors from both industry and academia, Numerical Methods for Finance explores new and relevant numerical methods for the solution of practical problems in finance. It is

Three engineering professors lay down the foundation of singular perturbation theory for linear and nonlinear systems, and illustrate the theory with solved examples and applications. This reprint of

The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers a

A visual, interdisciplinary approach to solving problems in numerical methods Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solution

Gives an introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductions on the subject, this work distinguishes between formal and r

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

Elementary yet rigorous, this concise treatment explores practical numerical methods for solving very general two-point boundary-value problems. The approach is directed toward students with a knowled

Applied Numerical Methods with MATLAB is written for students who want to learn and apply numerical methods in order to solve problems in engineering and science. As such, the methods are motivated by

Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for sol

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

This book brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. It is a compilation of ideas

Perturbation Methods for Engineers and Scientists examines the main techniques of perturbation expansions applied to both differential equations and integral expressions. It describes several fluid d

Penguins aren’t the only animal out there with problems, oh no…Praise for Penguin Problems: "A small philosophy manual for readers of all ages ... wonderfully original" ObserverFrom Jory John and Lane

《應用數值方法：使用 MATLAB®》(Applied Numerical Methods with MATLAB® for Engineers and Scientists, 4e) 淺顯易懂，而採用直譯語法的 MATLAB ，可利用簡易語法來呈現不同的數值計算結果 (甚至繪圖)，讓初學者領會各種數值方法的簡潔求解過程和答案的意義。本書另一個特色是多元的案例。許多章節附上各種工程應用類型的案例，

Covering many techniques widely used in research, this book will help researchers in the physical sciences and engineering solve troublesome - and potentially very time consuming - problems in their work. The book deals with technical difficulties that often arise unexpectedly during the use of various common experimental methods, as well as with human error. It provides preventive measures and solutions for such problems, thereby saving valuable time for researchers. Some of the topics covered are: sudden leaks in vacuum systems, electromagnetic interference in electronic instruments, vibrations in sensitive equipment, and bugs in computer software. The book also discusses mistakes in mathematical calculations, and pitfalls in designing and carrying out experiments. Each chapter contains a summary of its key points, to give a quick overview of important potential problems and their solutions in a given area.

This graduate-level text gives a self-contained exposition of fundamental topics in equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to standard subjects, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numerical methods. The second half of the book is devoted to nonequilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an important example. Kinetic theory receives a thorough treatment through analysis of the Boltzmann-Lorentz model and the Boltzmann equation. The book concludes with general nonequilibrium methods such as linear response, projection method and the Langevin and Fokker-Planck equations, including numerical simulation

Focusing on the conceptual understanding of mechanics, this exciting new text addresses developments in the methods of analyzing mechanics problems. It fully incorporates the highly sophisticated comp

Focusing on the conceptual understanding of mechanics, this exciting new text addresses developments in the methods of analyzing mechanics problems. It fully incorporates the highly sophisticated comp

How are the ice blocks of igloos so perfectly formed and fitted, andable, it's been said, to withstand the weight of a polar bear?

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is

Designed primarily for undergraduates, but also graduates and practitioners, this textbook integrates numerical methods and programming with applications from chemical engineering. Combining mathematical rigor with an informal writing style, it thoroughly introduces the theory underlying numerical methods, its translation into MATLAB programs, and its use for solving realistic problems. Specific topics covered include accuracy, convergence and numerical stability, as well as stiffness and ill-conditioning. MATLAB codes are developed from scratch, and their implementation is explained in detail, all while assuming limited programming knowledge. All scripts employed are downloadable, and built-in MATLAB functions are discussed and contextualised. Numerous examples and homework problems - from simple questions to extended case studies - accompany the text, allowing students to develop a deep appreciation for the range of real chemical engineering problems that can be solved using numerica

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 numeric

Brugnano and Iavernaro deal with the numerical solution of differential problems within the framework of geometric integration, a branch of numerical analysis that aims to devise numerical methods abl

This fourth in a suite of five practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical

This third in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical

The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop quali

"This book is an introduction to numerical methods for students in engineering. It covers solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems

This book is a revised and updated version, including a substantial portion of new material, of the authors' widely acclaimed earlier text "Perturbation Methods in Applied Mathematics". A new chapter

Borm (scientific computing, Christian-Albrechts U., Kiel, Germany) and Mehl (numerical mathematics, Technical U. of Berlin) present a number of the most important numerical methods for finding eigenva

NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second

Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems. Reflecting the author’s advances with Sinc since 1995, the text most notably provides a detai

Perturbation series expansion methods are sophisticated numerical tools used to provide quantitative calculations in many areas of theoretical physics. This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly correlated electron systems and elementary particles. Early chapters cover the classical treatment of critical phenomena through high-temperature expansions, and introduce graph theoretical and combinatorial algorithms. The book then discusses high-order linked-cluster perturbation expansions for quantum lattice models, finite temperature expansions, and lattice gauge models. Also included are numerous detailed examples and case studies, and an accompanying resources website, www.cambridge.org/9780521842426, contains programs for implementing these powerful numerical techniques. A valuable resource for graduate students and postdoctoral researchers work