剑桥出版社---偏微分方程数值解法

[复制链接]

字体大小: 正常放大

数学中国—罂粟

377 主题	148 听众	6033 积分

升级 20.66%

TA的每日心情

	奋斗 2016-7-14 13:54

签到天数: 219 天

[LV.7]常住居民III

群组: 2015年美赛冲刺

群组: 高等数学串讲

群组: 2014第三期英语写作

群组: SAS数据分析大赛冲刺

群组: 2015美赛优秀论文解析

电梯直达

1^#

发表于 2014-7-14 14:47 |只看该作者 |正序浏览

|招呼Ta 关注Ta

原版英文书第二版, g# I; f  {/ x0 r) N: P' V" W
contents:( _; o0 w  \5 @7 _
Preface to the first edition page viii5 @3 f, o% t3 }/ K3 r8 l+ }" }
Preface to the second edition xi
* u9 s6 o- W" B- [1 Introduction 1
2 Q4 c1 p/ l5 |1 E2 Parabolic equations in one space variable 78 x( n! E1 f5 H$ S: t
2.1 Introduction 7
1 q4 x# k/ a8 g5 J! P/ _2.2 A model problem 7
% C* e0 }5 T5 u9 W2.3 Series approximation 9" B. F! l. b! n. a! L
2.4 An explicit scheme for the model problem 10
5 s. L& |; s$ {. D8 Z: `2.5 Difference notation and truncation error 12
# \. v# S' o. k* V% X4 n4 y$ V7 u2.6 Convergence of the explicit scheme 16
/ p0 U! B  s- N& J1 C0 a5 G2.7 Fourier analysis of the error 19* M& S: s$ @* k; \6 T
2.8 An implicit method 22  Z) y; a; z' \
2.9 The Thomas algorithm 243 h, A. @: k& g' ?6 _- a5 A
2.10 The weighted average or θ-method 26
4 N' ]+ ?9 k0 d% d  l2.11 A maximum principle and convergence' U  G8 t6 s' i; j5 _( w
for μ(1−θ)≤ 1  X1 E" {3 |% D2 m* Z2 }# O3 ~" P
2 33
7 S& J; h- ^. A5 F6 Y( Z2.12 A three-time-level scheme 38
" F, o+ p6 ~! T  D! v5 z+ g2.13 More general boundary conditions 397 q2 K" g  O/ U' O: S/ F
2.14 Heat conservation properties 44
3 g) k" x0 W& r( `8 k' F. ?2.15 More general linear problems 46
" ~1 n1 W- ?+ c' H) n' _2.16 Polar co-ordinates 528 m' d2 `& a1 E7 X* E4 U, n$ T7 u4 w3 v
2.17 Nonlinear problems 540 C; m( G$ M+ t: M3 S* }
Bibliographic notes 56
9 {3 m6 N6 f4 P  h1 r! J$ wExercises 56
/ O- S8 Q& a# @$ \7 Sv
8 O* ]0 _# I) L6 Gvi Contents/ s% N/ y) i" G8 e: w  Z
3 2-D and 3-D parabolic equations 62/ ~) N4 f) v. V7 u
3.1 The explicit method in a rectilinear box 62
/ _6 O: B% i7 r& {+ j% r3.2 An ADI method in two dimensions 647 w/ E! A: N5 L: p
3.3 ADI and LOD methods in three dimensions 70
/ _% V/ k0 T- W& y4 }( @( }& P3.4 Curved boundaries 71* a; h  _9 X3 m/ M" K& }+ G0 N
3.5 Application to general parabolic problems 80
8 I& g. X, H& u' JBibliographic notes 83( D6 i, ?' o- W6 e3 Z$ P
Exercises 83
* K: x, s0 d2 t% n& }# o4 Hyperbolic equations in one space dimension 86
4 ?* A# X3 t- S# |5 C4.1 Characteristics 86
- b+ _; y  ~/ I/ j) F4.2 The CFL condition 89
* Q/ q) F1 L6 q$ m! F& G4.3 Error analysis of the upwind scheme 94# @$ x% b3 a0 Z8 m' G. T& w6 y: b
4.4 Fourier analysis of the upwind scheme 97
. N$ D* C( B6 ]0 U; h4.5 The Lax–Wendroff scheme 100. L- q  l! M# }3 x/ v9 L* [
4.6 The Lax–Wendroff method for conservation laws 103
7 H; B0 r9 l+ F6 [* d4.7 Finite volume schemes 110* q; a* P" }8 f
4.8 The box scheme 1163 f4 l6 C% x$ |0 b. o' Y3 s# }* M- N
4.9 The leap-frog scheme 1232 y4 g! \. |+ e! X) y4 k# g
4.10 Hamiltonian systems and symplectic4 |% ]. m3 ?- L9 o( c  o; \: L
integration schemes 128
* ]3 k  b& \5 b5 J& T0 J4.11 Comparison of phase and amplitude errors 135
$ E. l" D( M6 H. D, U: ?4.12 Boundary conditions and conservation properties 1394 S  |- [/ b' ~$ {- @4 X
4.13 Extensions to more space dimensions 1431 }# T6 r0 t) Y* w! T
Bibliographic notes 146
; s5 l- l  h2 Z5 O6 NExercises 146, M. a3 [+ l' r3 E  p
5 Consistency, convergence and stability 151
/ X4 v" R* O' x9 s8 l& G5.1 Definition of the problems considered 151
) X" E% i, M4 o5.2 The finite difference mesh and norms 152
( F4 V. G& {- _- r5.3 Finite difference approximations 1544 {! i, z2 t" Q0 |
5.4 Consistency, order of accuracy and convergence 156
3 }$ o  `+ j+ @+ X; ]1 D5.5 Stability and the Lax Equivalence Theorem 1570 f1 a! d$ H; `9 v, E* J% ?4 Q, P0 \
5.6 Calculating stability conditions 1609 ], x' L3 u( [' p
5.7 Practical (strict or strong) stability 1662 {: W" S5 O) B/ d4 H8 E
5.8 Modified equation analysis 169
, }- F5 g% y5 n8 N: a1 V3 b; U5.9 Conservation laws and the energy method of analysis 177
& p4 a2 A- N4 E6 r5.10 Summary of the theory 186
0 K! }7 I5 Y5 x* L, i4 n3 ]. @Bibliographic notes 189# M& S; O# _/ V! o
Exercises 190
  M1 \6 g- g( v$ z8 m7 c$ kContents vii9 g" a+ ?6 L0 C! Y9 G5 P
6 Linear second order elliptic equations in7 n* w; m$ e2 U+ U7 j9 ?/ D2 y
two dimensions 194
- M: A' C  ?- n6.1 A model problem 1944 P( E& a1 Y. V' J& {" R4 l: y/ w# b
6.2 Error analysis of the model problem 195
9 R: T4 [1 c! S9 B6.3 The general diffusion equation 197+ R  g& r9 o/ T! v
6.4 Boundary conditions on a curved boundary 1998 O& r. ~5 Z+ U/ P( w
6.5 Error analysis using a maximum principle 203
. Q0 ?% A+ \1 J  d$ r6.6 Asymptotic error estimates 213
9 i8 O* G' T. B1 ?; `4 V8 ?) l6.7 Variational formulation and the finite
0 U' w9 F, A) Celement method 2185 ]3 j! {  v/ D/ Y* G5 N
6.8 Convection–diffusion problems 224
. A  }8 i5 G6 n% T$ `6.9 An example 228( ^" K( H+ s( G$ O( l5 P
Bibliographic notes 231% O$ W; ?5 a6 N+ l# ]: ~5 j
Exercises 232
& B# c$ F+ c2 M, n; N4 E0 Q2 K) }7 Iterative solution of linear algebraic equations 235) k6 l; C) |% ]8 T/ {: i
7.1 Basic iterative schemes in explicit form 237
# ^7 V2 h. ?% s3 D4 D7.2 Matrix form of iteration methods and; D  A: k2 M, e& Q5 ~9 D7 r
their convergence 239
, z1 b5 j: D4 S8 M7.3 Fourier analysis of convergence 2445 T5 @7 K) a" D" I8 f  y
7.4 Application to an example 248
1 Y1 @# y7 {2 t4 q) K6 e/ }: M3 o' Z; g7.5 Extensions and related iterative methods 250* o& w) c7 c* [9 ^. U
7.6 The multigrid method 252
  S$ \) `6 Q4 Y" i; C* l7.7 The conjugate gradient method 258
  @9 r7 q$ k- K4 J% G* w7.8 A numerical example: comparisons 261: T( ~' p5 t7 ^5 e5 B* t% E+ p' V
Bibliographic notes 263
' l1 L4 b$ O9 f7 K$ d: ^; TExercises 263
% n1 q( B$ j9 _/ X( c9 ]References 2672 W, R2 W% l/ q$ _, _6 v9 A
Index 273