Computational Differential Equations

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Paperback | 4 November 1996 | Edition Number 2

At a Glance

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556 Pages

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22.86 x 15.24 x 2.87

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This is a two volume introduction to the computational solution of differential equations using a unified approach organized around the adaptive finite element method. It presents a synthesis of mathematical modeling, analysis, and computation. The goal is to provide the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modeling in science and engineering: How can we model physical phenomena using differential equations? What are the properties of solutions of differential equations? How do we compute solutions in practice? How do we estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The authors then widen the scope to cover the basic classes of linear partial differential equations modeling elasticity, heat flow, wave propagation and convection-diffusion-absorption problems. The book concludes with a chapter on the abstract framework of the finite element method for differential equations. Volume 2, to be published in early 1997, extends the scope to nonlinear differential equations and systems of equations modeling a variety of phenomena such as reaction-diffusion, fluid flow, many-body dynamics and reaches the frontiers of research. It also addresses practical implementation issues in detail. These volumes are ideal for undergraduates studying numerical analysis or differential equations. This is a new edition of a 1988 text of 275 pages by C. Johnson.

Industry Reviews

'... the aim of the book is succesfully attained, viz. to present a unified approach to computational mathematical modelling based on differential equations combining aspects of mathematics, computation and application.' G. Kirlinger, International Mathematical News 'The book is written in an accessible style and is well suited to serve as a basis for courses in mathematics, science and engineering.' Aslib Book Guide 'This is a well-written and highly readable book that should be useful for advanced undergraduates in Mathematics or for other scientists new to the field.' Mark Baldwin and Pijush Bhattacharyya, Mathematics Today ' ... provocative and should be taken seriously by all faculty, not just those in applied mathematics ... the ideas of the text could be used in many courses in analysis and computation ... this book provides a vision of computation and analysis that may become a model for the future.' Mathematics of Computation ' ... an excellent text ... a readable, up-to-date, easily accessible, and mathematically sound introduction to finite element methods ... a clear elucidation of the fundamentals of the finite element method at an elementary level.' Society for Industrial and Applied Mathematics ' ... delightful and illuminating ...' Journal of Fluid Mechanics

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Numerical Analysis Science Physics Classical Mathematics Fluid Mechanics

Introduction
Introduction
Review of calculus in one dimension
Piecewise polynomial approximation in one dimension
Review of linear algebra
A first example
Review of numerical linear algebra
Archetypes
An elliptic model problem
A parabolic model problem
A hyperbolic model problem
An elliptic-hyperbolic model problem
Systems of linear ode's
Calculus of variations
Computational mathematical modelling
Problems in Several Dimensions
Review of calculus in several dimensions
Elliptic problems
The heat equation
The wave equation
Stationary convection-diffusion
Time-dependent convection-diffusion
Eigenvalue problems
Power of abstraction
Appendix
History of calculus
Femlab
Table of Contents provided by Publisher. All Rights Reserved.

Computational Differential Equations

At a Glance

Paperback

Industry Reviews

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How to return your order

Defective items

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