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	5990 积分

升级 19.8%

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 |倒序浏览

|招呼Ta 关注Ta

原版英文书第二版& _  f6 T3 g- {( }( y7 l
contents:4 a* Z; S6 i7 G" k$ Q
Preface to the first edition page viii/ x( p5 `  u& H( D5 j
Preface to the second edition xi- r! V3 n+ `' R4 b- G, T
1 Introduction 1
' V9 B0 O: b1 {; l2 Parabolic equations in one space variable 7
8 `) H$ H. l* o/ h1 L2.1 Introduction 7
. K5 M% n7 X2 r7 _( h4 O1 P1 J2.2 A model problem 78 A) o- H3 M  [+ F6 [) a  C
2.3 Series approximation 9
% a) V3 o0 @; @( m: S2.4 An explicit scheme for the model problem 10
- ], ]! ^0 U1 W: S- y, A2.5 Difference notation and truncation error 121 x% q+ v' l) D
2.6 Convergence of the explicit scheme 16
. |4 ^2 Z9 j  u& h2.7 Fourier analysis of the error 199 V/ t% n" k% L' \8 l& \
2.8 An implicit method 22
# z) S/ W+ O+ `: [* p$ }2.9 The Thomas algorithm 24( a; i# d; S) r9 q7 o
2.10 The weighted average or θ-method 26& B- }+ r& b: @: d+ T
2.11 A maximum principle and convergence
4 Y# @: a7 I4 H" q9 s# @  n5 U  Nfor μ(1−θ)≤ 1
) L5 G: M( k' }  ?2 33" u9 U# U' l% W: z4 }
2.12 A three-time-level scheme 38
; y3 ~) \% n3 S# K2.13 More general boundary conditions 39
' q( R- l9 d7 U) M- [$ j- e- s! H2.14 Heat conservation properties 441 A; T" S% l/ o6 [9 Z# q
2.15 More general linear problems 46( n" s. I  Z4 K% e
2.16 Polar co-ordinates 52  m* f) X& r$ F
2.17 Nonlinear problems 54
2 ?7 e. g! j2 J* m! i% \- CBibliographic notes 560 d; _; Q  W! [1 {0 V- V  n& }
Exercises 56! @0 x% s3 [, h2 G) D) f2 E4 N+ i
v, M6 a/ P# ?  r8 u
vi Contents$ X% ~' W: i0 A; `
3 2-D and 3-D parabolic equations 62
8 {3 o* ~2 s2 g" M# F3 I3.1 The explicit method in a rectilinear box 62
0 V& ]* t4 m1 B; v4 x* n3.2 An ADI method in two dimensions 64, w% ^: W! E0 V. N: G+ H1 c$ Y8 g
3.3 ADI and LOD methods in three dimensions 70$ I7 z+ N# k8 R1 @& Y, K
3.4 Curved boundaries 71
4 ?+ v1 o- H2 r8 G9 W2 Z3.5 Application to general parabolic problems 80
& F9 i+ i' a$ O0 g; G; z' uBibliographic notes 83, @/ K" R4 M4 s5 m
Exercises 83
; h8 L9 R9 Z2 Z* z, F* N% o4 Hyperbolic equations in one space dimension 86+ D# `/ E# l9 Q; x$ r" L  ~
4.1 Characteristics 861 f+ K# m- e. S1 X+ F& v
4.2 The CFL condition 890 D- L6 u6 |, J- S( V4 T0 J" i
4.3 Error analysis of the upwind scheme 94/ a; w5 u8 }+ k. c
4.4 Fourier analysis of the upwind scheme 973 f' E  e( A& p  H
4.5 The Lax–Wendroff scheme 100
! ^( ~# ]" Q0 a( [4 V, _. B6 e( W4.6 The Lax–Wendroff method for conservation laws 103
9 M* g7 x) b3 u* d4.7 Finite volume schemes 110
+ X8 j/ w1 e4 Q2 D4 ]) y4.8 The box scheme 1166 Y9 ]' j9 S+ b2 E
4.9 The leap-frog scheme 123
- K3 z$ `# B: c2 Y. p" ~4.10 Hamiltonian systems and symplectic( H  Q" H) ?( p( k5 F- s: R. p
integration schemes 128
* K* n8 O; Q3 }  b" d4.11 Comparison of phase and amplitude errors 135& V7 ~7 o6 z5 l  K- V* ^" H4 n" ~
4.12 Boundary conditions and conservation properties 139/ k3 q# k9 f1 D) ^
4.13 Extensions to more space dimensions 143
  @1 r& _/ N5 M8 M* r6 XBibliographic notes 146, E3 d/ ^. R  T* p7 ~: ^# s5 c
Exercises 146
7 e4 M) M/ ^* {/ @5 Consistency, convergence and stability 151
6 X$ q$ e9 D8 L4 X+ G, T' B5.1 Definition of the problems considered 151- L' W  X: j4 g- C; n; `" ]) G
5.2 The finite difference mesh and norms 152
7 W1 }! \; p, s" T- h' A5 D5.3 Finite difference approximations 154
) P) G! x' t" n5.4 Consistency, order of accuracy and convergence 156
, b1 K9 u7 V) i0 D5.5 Stability and the Lax Equivalence Theorem 157) |! ]; b7 ^! N! {! r
5.6 Calculating stability conditions 160# R. ?, z& @5 [4 \( u- `5 u6 l6 F
5.7 Practical (strict or strong) stability 166+ f/ V; @  `' B' A
5.8 Modified equation analysis 169
4 T3 B; x, w9 r9 F( N5.9 Conservation laws and the energy method of analysis 1774 T3 n) L* i; j: K4 [6 s/ w
5.10 Summary of the theory 186
4 B  w7 `, a) A$ n( I* |Bibliographic notes 189& r; p9 v3 ?  `6 F; N+ {0 z' a
Exercises 190/ \" {! l1 s7 H$ t( r5 X
Contents vii
3 M2 w, O* c' Z1 R+ A2 w6 Linear second order elliptic equations in& s9 [2 Y# J. k8 c2 A7 O
two dimensions 1948 X+ B# ~4 z% M: o& g/ w5 p
6.1 A model problem 194- G$ U8 u& M3 [7 ?7 _9 B  Y
6.2 Error analysis of the model problem 195* L; ~- Z7 E* g" B* T
6.3 The general diffusion equation 1971 q  ]1 o5 M; v; o6 r
6.4 Boundary conditions on a curved boundary 199: N, W& {' ]3 n
6.5 Error analysis using a maximum principle 203
& }3 p$ V$ f5 s0 q7 m6 v" v6 j6.6 Asymptotic error estimates 213; g1 b6 L, X5 a/ T4 j3 y6 c
6.7 Variational formulation and the finite% R% p0 w3 g5 b  k2 i2 C
element method 218. U( B, J5 R, s
6.8 Convection–diffusion problems 224
7 C' f" o: y4 `8 V6.9 An example 228
5 l6 [9 ^% I5 o+ y3 d6 l# {Bibliographic notes 231
8 n. c# h# X( m! `& X3 r6 ~Exercises 232- ~) g& X$ Y% F3 f1 e3 i" M( r
7 Iterative solution of linear algebraic equations 235
0 y4 o* T$ B, G; [0 ~7.1 Basic iterative schemes in explicit form 237
( }( i) f- F1 f. q: @% z7.2 Matrix form of iteration methods and3 H& q+ |& K) q+ A( \3 D
their convergence 239, X2 g( `* x$ J- J% r
7.3 Fourier analysis of convergence 244
9 k0 |: V: m1 c, \7.4 Application to an example 2482 z' p' r+ d4 X2 _
7.5 Extensions and related iterative methods 250
' S) P' s: F8 Z+ |( ]+ C7.6 The multigrid method 252& C3 M1 ]6 [1 N( N3 B
7.7 The conjugate gradient method 258
+ h: o; p$ L! J9 l7.8 A numerical example: comparisons 261+ V* B/ `) v3 ~  U0 `5 z: O
Bibliographic notes 263
# h7 ]  G* t0 n- @4 |; hExercises 263
9 O; E- {; c0 b, \7 t6 V# T* W) ^References 267, V1 `( s4 t# e  y7 m( d" C
Index 273