Numerical Solution of Ordinary Differential Equations

✍ Scribed by Leon Lapidus and John H. Seinfeld (Eds.)

Publisher: AP
Year: 1971
Tongue: English
Leaves: 304
Series: Mathematics in Science and Engineering 74
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

✦ Table of Contents

Content:
Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages xi-xii

1 Fundamental Definitions and Equations
Pages 1-38

2 Runge-Kutta and Allied Single-Step Methods
Pages 39-106

3 Stability of Multistep and Runge-Kutta Methods
Pages 107-151

4 Predictor-Corrector Methods
Pages 152-241

5 Extrapolation Methods
Pages 242-266

6 Numerical Integration of Stiff Ordinary Differential Equations
Pages 267-293

Index
Pages 295-299

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