Numerical Solution of Partial Differential Equations

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface to the first edition page viii Preface to the second edition xi 1 Introduction 1 2 Parabolic equations in one space variable 7 2.1 Introduction 7 2.2 A model problem 7 2.3 Series approximation 9 2.4 An explicit scheme for the model problem 10 2.5 Difference notation and truncation error 12 2.6 Convergence of the explicit scheme 16 2.7 Fourier analysis of the error 19 2.8 An implicit method 22 2.9 The Thomas algorithm 24 2.10 The weighted average or θ-method 26 2.11 A maximum principle and convergence for µ(1 − θ) ≤ 1 2 33 2.12 A three-time-level scheme 38 2.13 More general boundary conditions 39 2.14 Heat conservation properties 44 2.15 More general linear problems 46 2.16 Polar coordinates 52 2.17 Nonlinear problems 54 Bibliographic notes 56 Exercises 56 v