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.
目录
Series Preface Preface Contents of Part 2: Conservation Laws and Elliptic Equations 0 Prelude 1 Introduction to Finite Differences 1.1 Introduction 1.2 Getting Started 1.3 Consistency 1.4 Neumann Boundary Conditions 1.5 Some Variations 1.6 Derivation of Difference Equations 2 Some Theoretical Considerations 2.1 Introduction 2.2 Convergence 2.3 Consistencey 2.4 Stability 2.5 The Lax Theorem 2.6 Computational Interlude I 3 Stability 3.1 Analysis of Stability 3.2 Finite Fourier Series and Stability 3.3 Gerschgorin Circle Theorem 3.4 Computional Interlude II 4 Parabolic Equations 4.1 Introduction 4.2 Two Dimensional Parabolic 4.3 Convergence, Consistency, Stability 4.4 Alternation Direction Implicit Schemes 4.5 Polar Coordinates 5 Hyperbolic Equations 5.1 Introducion 5.2 Initial-Value Problems 5.3 Numerical Solution of Initial-Value Problems 5.4 Implicit Schemes 5.5 Initial-Boundary-Value Problems 5.6 Numerical Solution of Initial-Boundary-Value Problems 5.7 The Courand-Friedrichs-Lewy Condition 5.8 Two Dimensional Hyperbolic Equations 5.9 Computational Interlude III 6 Systems of Partial Differential Equations 6.1 Introduction 6.2 Initial-Value Difference Schemes …… 7 Dispersion and Dissipation References Index
