Lutz Tobiska's Books

No detailed description available for "Singularly Perturbed Differential Equations".

An easy-to-understand guide covering the key principles of finite element methods and its applications to differential equations.

The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.

This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

From the reviews: "Astronomy and Astrophysics Abstracts has appeared in semi-annual volumes since 1969 and it has already become one of the fundamental publications in the fields of astronomy, astrophysics and neighbouring sciences. It is the most important English-language abstracting journal in the mentioned branches. ...The abstracts are classified under more than a hundred subject categories, thus permitting a quick survey of the whole extended material. The AAA is a valuable and important publication for all students and scientists working in the fields of astronomy and related sciences. As such it represents a necessary ingredient of any astronomical library all over the world." Space Science Reviews#1 "Dividing the whole field plus related subjects into 108 categories, each work is numbered and most are accompanied by brief abstracts. Fairly comprehensive cross-referencing links relevant papers to more than one category, and exhaustive author and subject indices are to be found at the back, making the catalogues easy to use. The series appears to be so complete in its coverage and always less than a year out of date that I shall certainly have to make a little more space on those shelves for future volumes." The Observatory Magazine#2

An easy-to-understand guide covering the key principles of finite element methods and its applications to differential equations.

No detailed description available for "Singularly Perturbed Differential Equations".

Book's by Lutz Tobiska

Singularly Perturbed Differential Equations

Singularly Perturbed Differential Equations

Finite Elements

Finite Elements

Numerical Methods for Singularly Perturbed Differential Equations

Numerical Methods for Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Literature 1988, Part 1

Literature 1988, Part 1

Finite Elements

Finite Elements

Robust Numerical Methods for Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations

Numerical Methods for Singularly Perturbed Differential Equations

Numerical Methods for Singularly Perturbed Differential Equations

Singularly Perturbed Differential Equations

Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations

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