Fitted Numerical Methods for Singular Perturbation Problems

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

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depen

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

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the

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

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

Differential games theory is the most appropriate discipline for the modelling and analysis of real life conflict problems.The theory of differential games is here treated with an emphasis on the cons

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

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

Mathematical physics equations, like some other problems, often require solving boundary value problems for partial differential equations. Attaining approximate solutions requires developing and exam

This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. While there are textbooks o

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

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerica

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 Matching Method for Asymptotic Solutions in Chemical Physics Problems by A. M. Il'in, L. A. Kalyakin, and S. I. MaslennikovSingularly Perturbed Problems with Boundary and Interior Layers: Theory a

The method of least squares is today the principal tool for reducing the influence of errors when fitting models to given observations. This volume gives an in-depth treatment of topics such as method

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