Difference Schemes: An Introduction to the Underlying Theory

✍ Scribed by S.K. Godunov and V.S. Ryabenkii (Eds.)

• Publisher: Elsevier Science Ltd
• Year: 1987
• Tongue: English
• Leaves: 509
• Series: Studies in Mathematics and Its Applications 19
• Edition: 2nd ed.
• Category: Library

✦ Synopsis

Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes. This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists. While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.

✦ Table of Contents

Content:
Edited by
Pages ii-iii

Copyright page
Page iv

Preface
Pages v-vii

Introduction
Pages 1-4

Chapter 1 Difference Equations of first and Second order
Pages 5-30

Chapter 2 Boundary-Value Problems for Equations of Second Order
Pages 31-52

Chapter 3 Some Basic Methods for the Study of Stability
Pages 53-69

Chapter 4 Elementary Examples of Difference Schemes
Pages 71-81

Chapter 5 Convergence of the Solutions of Difference Equations as a Consequence of Approximation and Stability
Pages 83-167

Chapter 6 widely-Used Difference Schemes
Pages 169-183

Chapter 7 Simplest Examples of the Construction and Study of Difference Schemes
Pages 185-239

Chapter 8 Some Basic Methods for the Study of Stability
Pages 241-291

Chapter 9 Difference Scheme Concepts in the Computation of Generalized Solutions
Pages 293-308

Chapter 10 The Concept of Difference Schemes with Splitting
Pages 309-324

Chapter 11 Elliptic Problems
Pages 325-356

Chapter 12 Concept of Variational-Difference and Projection-Difference Schemes
Pages 357-390

Chapter 13 Construction of the Transition Operator
Pages 392-431

Chapter 14 Spectral Criterion for the Stability of Nonselfadjoint Bvolutional Boundary-Value Problems
Pages 433-459

Appendix Method of Internal Boundary Conditions
Pages 461-473

Bibliographical Commentaries
Pages 475-481

Bibliography Review Article
Pages 483-484

Index
Pages 485-489