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
6 w: l4 v: k) k9 s) RPreface to the second edition xi
( o) H; x+ ]3 l2 H- J4 g* j1 ^1 Introduction 1
+ X7 z' B0 ?$ n& ^/ E2 Parabolic equations in one space variable 7
& ], s& r( E! l, v' }5 n0 p1 T, x2.1 Introduction 7
7 Q8 r4 B" E+ Y; L( E4 I2.2 A model problem 7
2.3 Series approximation 9
2 ]& c  a, n$ Z. d2 @. r2.4 An explicit scheme for the model problem 10
% _* {8 ~  ?% g" |) u) g2.5 Difference notation and truncation error 12
2.6 Convergence of the explicit scheme 16
$ |5 b' z: J& _/ L+ [: u- C0 @* k2.7 Fourier analysis of the error 19
7 R7 @' l& B% N9 M: b2.8 An implicit method 22
, ]3 s: A( ~* h' }4 ?8 H2.9 The Thomas algorithm 24
0 o4 a- V+ s, D& O$ Q2.10 The weighted average or θ-method 26
4 F; w0 n+ W3 k- P4 h9 T2.11 A maximum principle and convergence
6 T  m9 P  h+ z  }2 Nfor μ(1−θ)≤ 1
& d$ D8 v# u1 x: a0 i5 O8 t2 33
2.12 A three-time-level scheme 38
  r# j! B8 P% n& b0 L2.13 More general boundary conditions 39
2.14 Heat conservation properties 44
7 [8 Z! ]2 a! j* F+ b7 C# u6 w2.15 More general linear problems 46
8 H: C% z) d2 `+ J% P4 d2.16 Polar co-ordinates 52
/ \  J( Y+ p! i- g. \2.17 Nonlinear problems 54
7 Y4 L& r5 b+ BBibliographic notes 56
; E: t, a. u* ^3 F; y. v' _: `Exercises 56
v
vi Contents
8 ]- H2 p/ _* s/ O3 }3 l3 2-D and 3-D parabolic equations 62
3.1 The explicit method in a rectilinear box 62
  |. Q* t3 l5 R3.2 An ADI method in two dimensions 64
* i0 R# L7 }% Y; _0 f; D9 `3.3 ADI and LOD methods in three dimensions 70
3.4 Curved boundaries 71
8 {" I0 j' x9 j( {3.5 Application to general parabolic problems 80
Bibliographic notes 83
2 c, Y3 z: \' [8 P# \+ g3 X- TExercises 83
4 Hyperbolic equations in one space dimension 86
4.1 Characteristics 86
4.2 The CFL condition 89
/ g8 |( v5 m& O$ A  d" ?4.3 Error analysis of the upwind scheme 94
4 l' r  V6 ]* {# q4.4 Fourier analysis of the upwind scheme 97
4.5 The Lax–Wendroff scheme 100
$ j/ ^" x1 O; }$ B4.6 The Lax–Wendroff method for conservation laws 103
1 ]% I  @% @5 b# y" v; a& b4.7 Finite volume schemes 110
0 W7 b6 I  o( `/ ]5 \: m' I" Q; E4.8 The box scheme 116
4.9 The leap-frog scheme 123
5 `: n) s- a/ h0 }4.10 Hamiltonian systems and symplectic
integration schemes 128
4.11 Comparison of phase and amplitude errors 135
4.12 Boundary conditions and conservation properties 139
5 v. w: f- u! S5 d4.13 Extensions to more space dimensions 143
7 H0 H) D7 Q+ q% z9 sBibliographic notes 146
+ B3 }+ o$ U& l% K; u7 e- y; ^Exercises 146
5 Consistency, convergence and stability 151
5.1 Definition of the problems considered 151
5.2 The finite difference mesh and norms 152
5.3 Finite difference approximations 154
. x0 E8 x3 ~7 X( ?: N5.4 Consistency, order of accuracy and convergence 156
- [4 B+ w, _4 T5.5 Stability and the Lax Equivalence Theorem 157
5.6 Calculating stability conditions 160
3 a9 f, D/ J* ^/ i9 h5.7 Practical (strict or strong) stability 166
2 \0 y6 o( g5 m8 V3 y5.8 Modified equation analysis 169
2 a" R+ d4 a) S( m% w" O5.9 Conservation laws and the energy method of analysis 177
5.10 Summary of the theory 186
Bibliographic notes 189
Exercises 190
Contents vii
6 Linear second order elliptic equations in
two dimensions 194
6.1 A model problem 194
6.2 Error analysis of the model problem 195
6.3 The general diffusion equation 197
4 i. Y/ ^& s) @0 n6.4 Boundary conditions on a curved boundary 199
, `, ^' o; n) L% P# l6.5 Error analysis using a maximum principle 203
; J2 Z. i, D! T; R6.6 Asymptotic error estimates 213
6.7 Variational formulation and the finite
3 F6 Y( R/ `, F# K. p& P( ^6 i; Selement method 218
6.8 Convection–diffusion problems 224
0 J% M" H5 m+ V; y0 w$ e) q* C6.9 An example 228
* i( S. X8 j% }: ]Bibliographic notes 231
Exercises 232
7 Iterative solution of linear algebraic equations 235
7.1 Basic iterative schemes in explicit form 237
7.2 Matrix form of iteration methods and
( x/ N/ F3 D. ]# T. ?" D: k" btheir convergence 239
7.3 Fourier analysis of convergence 244
) v  {5 M" u$ t* Y2 M' M, C7.4 Application to an example 248
7.5 Extensions and related iterative methods 250
7.6 The multigrid method 252
6 T( d0 h# Z$ g2 t8 S4 M7.7 The conjugate gradient method 258
8 w1 u1 |3 v) o0 m' ~. J0 I2 b7.8 A numerical example: comparisons 261
Bibliographic notes 263
Exercises 263
) Q7 ?" H# h1 q) QReferences 267
+ S  y; @8 b& ?7 tIndex 273

% b) h3 `, m" l

游客，如果您要查看本帖隐藏内容请回复

3 @$ N6 C( @% {( {8 _* L) M+ d+ ]

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

4 i8 h. b) B; b9 D& Y

chqu12

宇仲

很不错的，鼓励共享。

数学问题

很好耶O(∩_∩)O哈哈哈~