| 查看: 5991 | 回复: 87 | |||||||||||||
| 【奖励】 本帖被评价82次，作者louyc增加金币 65.4 个 | |||||||||||||
| 当前只显示满足指定条件的回帖，点击这里查看本话题的所有回帖 | |||||||||||||
[资源]
剑桥出版社---偏微分方程数值解法
|
|||||||||||||
|
原版英文书 第二版 contents: Preface to the first edition page viii Preface to the second edition xi 1 Introduction 1 2 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 2.5 Difference notation and truncation error 12 2.6 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 2.11 A maximum principle and convergence for μ(1−θ)≤ 1 2 33 2.12 A three-time-level scheme 38 2.13 More general boundary conditions 39 2.14 Heat conservation properties 44 2.15 More general linear problems 46 2.16 Polar co-ordinates 52 2.17 Nonlinear problems 54 Bibliographic notes 56 Exercises 56 v vi Contents 3 2-D and 3-D parabolic equations 62 3.1 The explicit method in a rectilinear box 62 3.2 An ADI method in two dimensions 64 3.3 ADI and LOD methods in three dimensions 70 3.4 Curved boundaries 71 3.5 Application to general parabolic problems 80 Bibliographic notes 83 Exercises 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 4.4 Fourier analysis of the upwind scheme 97 4.5 The Lax–Wendroff scheme 100 4.6 The Lax–Wendroff method for conservation laws 103 4.7 Finite volume schemes 110 4.8 The box scheme 116 4.9 The leap-frog scheme 123 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 4.13 Extensions to more space dimensions 143 Bibliographic notes 146 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 5.4 Consistency, order of accuracy and convergence 156 5.5 Stability and the Lax Equivalence Theorem 157 5.6 Calculating stability conditions 160 5.7 Practical (strict or strong) stability 166 5.8 Modified equation analysis 169 5.9 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 6.4 Boundary conditions on a curved boundary 199 6.5 Error analysis using a maximum principle 203 6.6 Asymptotic error estimates 213 6.7 Variational formulation and the finite element method 218 6.8 Convection–diffusion problems 224 6.9 An example 228 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 their convergence 239 7.3 Fourier analysis of convergence 244 7.4 Application to an example 248 7.5 Extensions and related iterative methods 250 7.6 The multigrid method 252 7.7 The conjugate gradient method 258 7.8 A numerical example: comparisons 261 Bibliographic notes 263 Exercises 263 References 267 Index 273 |
回复此楼» 本帖附件资源列表
-
欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com - 附件 1 : Morton_K_Numerical_solution_of_partial_differential_equations.._an_introduction_(2ed.,_CUP,_2005)(ISBN_0521607930)(293s).pdf
2014-01-05 04:07:30, 3.96 M
» 收录本帖的淘帖专辑推荐
 专业书籍（外文版）WM | 淘贴淘宝 | 计算数学与经济统计 | 我的文件——值得收藏 |
| 新发现 | 待下载 | 资源收藏 | 已成功下载 |
| 个人收藏书吧 | 数学 | 计算 |
» 猜你喜欢
309求调剂
已经有8人回复
-
一志愿南航 335分 | 0856 | GPA 4.07 | 有科研经历
已经有8人回复
-
求调剂
已经有5人回复
-
求化学调剂
已经有5人回复
-
085600，材料与化工321分求调剂
已经有10人回复
-
0703 化学 求调剂，一志愿山东大学 342 分
已经有5人回复
-
一志愿南开大学0710生物学359求调剂
已经有3人回复
-
085600，专业课化工原理，320分求调剂
已经有4人回复
-
材料与化工272求调剂
已经有16人回复
-
290求调剂
已经有3人回复
» 本主题相关价值贴推荐，对您同样有帮助:
3楼2014-01-06 00:15:20
8楼2014-01-06 14:55:14
简单回复
applaq2楼
2014-01-05 17:50
回复
五星好评 顶一下，感谢分享！
anzaigtt4楼
2014-01-06 08:42
回复
五星好评 顶一下，感谢分享！
2014-01-06 10:28
回复
五星好评 顶一下，感谢分享！
2014-01-06 12:15
回复
五星好评 顶一下，感谢分享！
2014-01-06 14:19
回复
五星好评 顶一下，感谢分享！
tryhard9楼
2014-01-06 17:21
回复
五星好评 顶一下，感谢分享！
难得糊涂10010楼
2014-01-06 19:27
回复
五星好评 顶一下，感谢分享！
lxwqd11楼
2014-01-06 20:06
回复
五星好评 顶一下，感谢分享！
周末不早起12楼
2014-01-06 21:40
回复
五星好评 顶一下，感谢分享！
tips12313楼
2014-01-08 21:54
回复
五星好评 顶一下，感谢分享！
wmnick14楼
2014-01-08 22:53
回复
五星好评 顶一下，感谢分享！
