剑桥出版社---偏微分方程数值解法

数学中国—罂粟

原版英文书 第二版
contents:
Preface to the first edition page viii
% @; o* s8 z' H# }% ]3 SPreface to the second edition xi
/ I; ~2 B9 S+ V1 Introduction 1
5 G$ \! l* N' I6 ]' q- ]' j, [5 g2 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
4 }* h5 A) \0 x' [/ M$ Q/ [2 W7 C2.5 Difference notation and truncation error 12
$ N/ F3 K2 y! O) m2.6 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
, I6 e! O* M  v2.11 A maximum principle and convergence
5 E0 J* a* t% v' F% ^8 ufor μ(1−θ)≤ 1
. f# x7 b3 D2 G$ N  n( B2 33
2.12 A three-time-level scheme 38
% D/ {0 C% @$ x# J% u7 ?. |  K& V+ X2.13 More general boundary conditions 39
2.14 Heat conservation properties 44
2.15 More general linear problems 46
2.16 Polar co-ordinates 52
8 v) X2 h% g1 o' N9 o9 [2.17 Nonlinear problems 54
Bibliographic notes 56
9 ?/ K& H$ u! G7 E! r3 dExercises 56
v
9 ?& q( {+ S% z1 c% Lvi Contents
3 2-D and 3-D parabolic equations 62
" D5 e: n3 O1 P% U* M# n; S3.1 The explicit method in a rectilinear box 62
* W3 C" |+ n& m1 D% ?% `) y3.2 An ADI method in two dimensions 64
3.3 ADI and LOD methods in three dimensions 70
/ q0 j- O1 [9 m/ x' }7 M3.4 Curved boundaries 71
; N2 J, |; ]4 p% p- A3.5 Application to general parabolic problems 80
+ G8 ]( Z5 f0 ?Bibliographic notes 83
4 t$ a% {8 y2 i  l, K) CExercises 83
4 Hyperbolic equations in one space dimension 86
4.1 Characteristics 86
4.2 The CFL condition 89
4.3 Error analysis of the upwind scheme 94
! s6 X% n4 S6 \0 _, g7 Y- Y% s4.4 Fourier analysis of the upwind scheme 97
9 D# e! B( [8 F' X6 g4.5 The Lax–Wendroff scheme 100
% y+ E7 B* v, Y4.6 The Lax–Wendroff method for conservation laws 103
* L) m. `. d+ G2 W5 P0 |( f. i4.7 Finite volume schemes 110
4.8 The box scheme 116
" D. K! ?$ x; M  h9 Z' m4.9 The leap-frog scheme 123
& K5 ~! [: J7 W* S) i3 h4.10 Hamiltonian systems and symplectic
integration schemes 128
) K- R4 O6 b4 S) ^  w$ s3 u5 n4.11 Comparison of phase and amplitude errors 135
4.12 Boundary conditions and conservation properties 139
" L- d9 y8 L/ @4.13 Extensions to more space dimensions 143
Bibliographic notes 146
Exercises 146
6 F1 R8 O  Q5 d$ j2 V& C) |5 Consistency, convergence and stability 151
5.1 Definition of the problems considered 151
- a; Q9 ~5 r& t+ Y5.2 The finite difference mesh and norms 152
5.3 Finite difference approximations 154
5.4 Consistency, order of accuracy and convergence 156
" n+ ~1 P1 Z9 G8 l8 K* B, p5.5 Stability and the Lax Equivalence Theorem 157
  U( d$ W+ A$ u1 d5.6 Calculating stability conditions 160
) ~5 o1 c& z5 ]8 ^6 v$ d5.7 Practical (strict or strong) stability 166
6 ~3 i. T) K( m6 R# V- Y* o5.8 Modified equation analysis 169
5.9 Conservation laws and the energy method of analysis 177
6 Z, P1 q  K0 K" e" u3 ]5.10 Summary of the theory 186
  ~2 E5 m4 i) F2 m# \Bibliographic notes 189
Exercises 190
) |2 }6 P: C9 w* b1 x5 X9 ?Contents vii
6 Linear second order elliptic equations in
, B, ]- k8 H- o* _4 g2 B: Stwo dimensions 194
6.1 A model problem 194
# l, S8 W. x; `% a7 `* W6.2 Error analysis of the model problem 195
1 g# l; m0 G6 R4 u/ z% E6.3 The general diffusion equation 197
; \  Y* X  R- F6.4 Boundary conditions on a curved boundary 199
' m! V( q5 A  E5 b9 f6.5 Error analysis using a maximum principle 203
) @5 S) ^2 p  [9 Q- @9 z. w1 S' h6.6 Asymptotic error estimates 213
6.7 Variational formulation and the finite
element method 218
4 u, ~8 T% i2 v3 h* I+ _6.8 Convection–diffusion problems 224
6.9 An example 228
Bibliographic notes 231
; l3 w/ z6 G1 {3 |* J1 ZExercises 232
$ D, Z; r3 q+ o6 \, x3 M1 ]7 Iterative solution of linear algebraic equations 235
- _" k6 q8 p" `, P9 b5 K7.1 Basic iterative schemes in explicit form 237
4 Q  `2 \5 d- g5 U7 g7.2 Matrix form of iteration methods and
their convergence 239
7.3 Fourier analysis of convergence 244
+ D; `- V1 L0 V2 [  V' L7.4 Application to an example 248
; \: h! S, s0 f4 X; Z& }7.5 Extensions and related iterative methods 250
7.6 The multigrid method 252
7.7 The conjugate gradient method 258
4 U& ]6 q/ U' ^+ S7.8 A numerical example: comparisons 261
6 ^* {+ i" j* }/ u; sBibliographic notes 263
- S4 a, m. p! c4 S4 cExercises 263
6 H0 W0 N# Z) CReferences 267
Index 273

游客，如果您要查看本帖隐藏内容请回复

+ `3 z$ Q( ]0 G( L: f' E( @' g# i

" v9 A# U  A% R0 Y0 e& X

模天大楼

很好耶O(∩_∩)O哈哈哈~

模天大楼

很好耶O(∩_∩)O哈哈哈~

模天大楼

很好耶O(∩_∩)O哈哈哈~

数学中国YY主管

非常有用的资源，大家可以看看

LYJA

好，楼主辛苦了！。。。。。。。。

chqu12

chqu12

* b! O$ V. F6 F5 n5 a3 i

宇仲

很不错的，鼓励共享。
( D7 }, N! j8 j: H- c

数学问题

很好耶O(∩_∩)O哈哈哈~