偏微分方程的數(shù)值方法

內(nèi)容概要

本書分為兩卷（或者稱為兩部分），分別列入Springer《應(yīng)用數(shù)學(xué)叢書》之22卷和33卷，內(nèi)容取自作者在克羅拉多州立大學(xué)所開(kāi)的研究生課程講義，該課程講授偏微分方程的差分解法，授課的對(duì)象為應(yīng)用數(shù)學(xué)和工程專業(yè)的研究生。    本書的特點(diǎn)是強(qiáng)調(diào)實(shí)際上機(jī)操作，閱讀本書需要一定的偏微分方程基礎(chǔ)知識(shí)和編程能力，本書可以作為研究生和高年級(jí)大學(xué)生學(xué)習(xí)計(jì)算數(shù)學(xué)的教科書。第1卷《數(shù)值偏微分方程——有限差分法》（Numerical Partial Differential Equations: Finite Difference Methods）已購(gòu)權(quán)影印出版，編號(hào)為WB3299。

書籍目錄

Series Preface. Preface Preface to Part 1 Contents of Part 1 Stability of Initial-Boundary-Value Schemes   8.1 Introduction   8.2 Stability     8.2.1 Stability: An Easy Case     8.2.2 Stability: Another Easy Case     8.2.3 GKSO: General Theory     8.2.4 Left Quarter Plane Problems   8.3 Constructing Stable Difference Schemes   8.4 Consistency and Convergence     8.4.1 Norms and Consistency     8.4.2 Consistency of Numerical Boundary Conditions     8.4.3 Convergence Theorem: Gustafsson   8.5 Schemes Without Numerical Boundary Conditions   8.6 Parabolic Initial-Boundary-Value Problems 9 Conservation Laws   9.1 Introduction   9.2 Theory of Scalar Conservation Laws  9.3 Thepry of Sytems of Conservation Laws  9.4 Computational Interlude VI  9.5 Numercai Solution of Conservation Laws  9.6 Diffference Schemes for Conservation Laws  9.7 Difference Schemes for Scalar Conservation Laws  9.8 Difference Schemes for K-System Conservation Laws  9.9 Godunov Schemes  9.10 High Resolution Shcemes for Linear K-System  9.11 Implicit Schemes  ……10 Elliptic Equations11 Irregular Regions and GridsReferencesIndex

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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest'in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in AppliedMathe- rustics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses.　　此書為英文版。

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