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原版英文书第二版
/ Q* n. H8 x* Y! i- D8 V  p. tcontents:
% ]) @8 \: `* T! fPreface to the first edition page viii5 V1 F, S  U3 J( t2 v0 k
Preface to the second edition xi# C9 w5 ]5 C1 u5 e$ D
1 Introduction 1
5 I, ?+ D4 O0 f2 Parabolic equations in one space variable 7
5 |1 d6 q6 N* i2.1 Introduction 7# A# k' a, \# d6 C
2.2 A model problem 7
5 t7 K& }; I: H( S5 ?2.3 Series approximation 9% X+ C  F1 w3 v& G) d% L
2.4 An explicit scheme for the model problem 10
4 K3 ^8 ~/ a4 v3 V2.5 Difference notation and truncation error 12
( y& L& ~6 x" m' E9 c- I& N! N/ n2.6 Convergence of the explicit scheme 16& L* S# S4 v- N* V+ [$ u
2.7 Fourier analysis of the error 19
0 c7 `5 A* f/ J, c  }8 d/ D! _2.8 An implicit method 22. J  S9 H* ^: M( t  B
2.9 The Thomas algorithm 24
+ i& @1 h4 q; H* F0 s) k% i) Y7 K2.10 The weighted average or θ-method 26
& j; H/ t0 ]- I/ b% l; ^' ~2.11 A maximum principle and convergence8 t8 |5 w3 H- s& b- w% w
for μ(1−θ)≤ 1$ m* v' f4 N& H
2 33: ^" D$ F$ H3 X7 ~5 }+ N! V0 C
2.12 A three-time-level scheme 387 \' I3 M: t6 m( g( ]( b) c$ D
2.13 More general boundary conditions 39$ W" L$ ]( W. \( p& y* Z# l7 B2 k
2.14 Heat conservation properties 44
1 K! x) G% i' @2.15 More general linear problems 46
( }* d- C( f9 ^/ I( M# }( K2.16 Polar co-ordinates 52
. U3 c% I  L1 R8 C; ^# e$ N2.17 Nonlinear problems 54
/ b4 P: p" j4 M% P! F/ ^Bibliographic notes 56# n+ Z, b' x7 Z7 S/ j7 [
Exercises 56  V+ ~. X6 M  Q* g  B1 V6 C9 ~
v4 O+ `4 U2 M$ \5 s5 N* A2 s3 Z( g( R3 Y
vi Contents, U8 k! `; g7 A" M
3 2-D and 3-D parabolic equations 62; \, c- s% B- H
3.1 The explicit method in a rectilinear box 62) }3 I/ F9 h3 F9 t! u; Z2 b
3.2 An ADI method in two dimensions 64
! k. z5 z( D- L7 Q4 F3.3 ADI and LOD methods in three dimensions 70  ]+ Z+ S# T3 ^# n6 k: ?+ A* p
3.4 Curved boundaries 71- l* o2 `9 `6 p8 X) J; G. K9 J
3.5 Application to general parabolic problems 80
' D/ t& G; R  ?9 GBibliographic notes 833 M, m7 ^' d! K9 A* G
Exercises 832 \/ o, c; O/ U  [8 `$ I
4 Hyperbolic equations in one space dimension 86
# x2 k, u1 b4 e3 y- j8 f" u4.1 Characteristics 86" v) f! f# d$ v! K* a4 `7 A
4.2 The CFL condition 89* k& H. m& d$ p
4.3 Error analysis of the upwind scheme 94( l" [# H6 A* g5 I
4.4 Fourier analysis of the upwind scheme 977 ]7 O$ o8 y- i8 d, H/ I' S+ v
4.5 The Lax–Wendroff scheme 1003 z) U3 k, t+ C% ~/ a7 ?
4.6 The Lax–Wendroff method for conservation laws 103
5 B! I& S* u8 N4.7 Finite volume schemes 110& E! K- v2 `. P7 m* U
4.8 The box scheme 116# Y8 m) g4 P" o; y
4.9 The leap-frog scheme 123
0 K) l' k: G* a6 ]- h3 Z4 T3 D4.10 Hamiltonian systems and symplectic* ^' l6 }# ]0 S4 m$ K% e
integration schemes 128
; M: P' z8 R8 m9 L4.11 Comparison of phase and amplitude errors 135& r4 H3 o6 X7 G! S3 B1 g8 D
4.12 Boundary conditions and conservation properties 139- c: ]% j; ^" m0 R) x- z- I
4.13 Extensions to more space dimensions 1435 T+ A* ^0 ~7 s5 U3 d, i0 R
Bibliographic notes 146
1 Z3 B. x: d( N) R) H* ]& tExercises 146) [9 P" p) Q1 Y" W% W9 S( Y1 Z6 h" l
5 Consistency, convergence and stability 151
8 ^; F5 ]$ o; _4 g2 h5.1 Definition of the problems considered 151# o  Z* |/ ?: l1 L
5.2 The finite difference mesh and norms 152
) f: d8 \6 Y# O6 k, ?' B5.3 Finite difference approximations 154) [6 {8 \6 ~% o- s
5.4 Consistency, order of accuracy and convergence 156
1 q+ T( e0 N# ~$ S5 `# V" m! a7 z3 P5.5 Stability and the Lax Equivalence Theorem 1570 D8 K: q+ z( T- P0 a
5.6 Calculating stability conditions 160
( q( w( C' o! X7 k) `5 |5.7 Practical (strict or strong) stability 166$ E8 m/ ?1 s- v
5.8 Modified equation analysis 169
$ L( h; Q) Y, u# q: |5.9 Conservation laws and the energy method of analysis 177
" M8 B4 e( `5 ~6 X$ z/ o, Y5.10 Summary of the theory 186
7 K" J& ?* k3 {6 m  ?% x8 VBibliographic notes 1896 m, T$ v7 K+ s% g5 ^
Exercises 1905 n$ j! d( ^& z' f
Contents vii* @# [1 z* B5 l2 S' @
6 Linear second order elliptic equations in
; S* |, w% @5 I3 E, m8 m7 u9 htwo dimensions 194
8 _2 _$ y! T1 u6 f' w4 e6.1 A model problem 194( i2 G. p6 ~1 `9 u* T3 e' g( R
6.2 Error analysis of the model problem 1958 \; S  r8 K3 W4 s5 ~9 S
6.3 The general diffusion equation 197
0 W2 v+ y3 L: l( o: y: s( o9 n: {4 s6.4 Boundary conditions on a curved boundary 199
0 g& {6 s. y& M& G. z- L# U6.5 Error analysis using a maximum principle 203
, M9 L3 T4 d5 F1 s" f. W6.6 Asymptotic error estimates 213
3 K( X( J6 f7 V7 @4 [2 D+ a6.7 Variational formulation and the finite$ D( T7 e3 {6 W" e- H1 q& d
element method 218
" u! _2 G( ~2 L4 R/ Z$ V  h6.8 Convection–diffusion problems 224
( Q/ t- U  i4 E6.9 An example 228; t" O7 z% v. ]
Bibliographic notes 2312 @, Q0 ?: U1 B! P& S
Exercises 2329 y- I8 c- E4 ^: ?4 A2 F8 C
7 Iterative solution of linear algebraic equations 235) z: @7 ]8 B5 ~) B; F+ _
7.1 Basic iterative schemes in explicit form 237
% g& H/ q5 w8 S9 a  L7.2 Matrix form of iteration methods and. K! B, e/ c3 x7 [7 j5 I+ |
their convergence 239% F, y* Q! ?( T2 S7 ~3 d
7.3 Fourier analysis of convergence 244
* H- H6 X( X* `* ]! ^6 U/ I7.4 Application to an example 248. \1 ], _" r; i/ j8 k! Z* U) Z
7.5 Extensions and related iterative methods 250- G0 ]: A- q( h( r+ O. O, k
7.6 The multigrid method 252
/ V" j* {( D( ^; g& h7.7 The conjugate gradient method 258+ M: J9 @$ L7 ?2 j1 c5 N; z1 y
7.8 A numerical example: comparisons 2617 D6 p7 G& B6 @6 T) n) Z  ^
Bibliographic notes 263
8 r* F+ Y# C$ ^) g  L; d; ^. l/ XExercises 263( X7 r3 r7 n6 f, p4 X( X
References 267* \- z( ~: @9 J% G3 T
Index 273