圖書信息
出版社: 科學出版社; 第1版 (2006年12月1日)
叢書名: 國外數學名著系列
平裝: 614頁
開本: 16
ISBN: 7030166817
條形碼: 9787030166814
尺寸: 23.9 x 17 x 3.3 cm
重量: 1.1 Kg
作者簡介
作者：(瑞士)海爾
內容簡介
《常微分方程的解法2(剛性與微分代數問題)(第2版)(影印版)》共分四章，第一章介紹剛性問題的單步和外插法，第二章講述剛性問題的多步方法和一般線性方法，第三章討論奇異擾動問題的處理，第四章論述微分代數方程及其在約束力學系統中的套用。《常微分方程的解法2(剛性與微分代數問題)(第2版)(影印版)》每一章從介紹方法開始，依次討論實際套用、數值結果、階和精度的理論分析，線性和非線性穩定性、收斂性和漸近展開。剛性問題和微分代數問題來源於科學計算的各個方面(如物理、化學、生物、控制工程、電網分析及力學系統)。《常微分方程的解法2(剛性與微分代數問題)(第2版)(影印版)》包含了這些方面的各種套用及電腦程式。
目錄
Chapter IV. Stiff Problems——One-step Methods
IV.1 Examples of Stiff Equations
IV.2 Stability Analysis for Explicit RK Methoods
IV.3 Stability Function of Implicit RK-Methods
IV.4 Order Stars
IV.5 Construction of Implicit Runge-Kutta Methods
IV.6 Diagonally Implicit RK Methods
IV.7 Rosenbrock-Type Methods
IV.8 Implementation of Implicit Runge-Kutta Methods
IV.9 Extrapolation Methods
IV.10 Numerical Experiments
IV.11 Contractivity for Linear Problems
IV.12 B-Stability and Contractivity
IV.13 Positive Quadrature Formulas and B-Stable RK-Methods
IV.14 Existence and Uniqueness of irk Solutions
IV.15 B-Convergence
Chapter V. Multistep Methods for Stiff Problems
V.1 Stability of Multistep Methods
V.2 "Nearly" A-Stable Multistep Methods
V.3 Generalized Multistep Methods
V.4 Order Stars on Riemann Surfaces
V.5 Experiments with Multistep Codes
V.6 One-Leg Methods and G-Stability
V.7 Convergence for Linear Problems
V.8 Convergence for Nonlinear Problems
V.9 Algebraic Stability of General Linear Methods
Chapter VI. Singular Perturbation Problems and Index 1 Problems
VI.1 Solving Index 1 Problems
VI.2 Multistep Methods
VI.3 Epsilon Expansions for Exact and RK Solutions
VI.4 Rosenbrock Methods
VI.5 Extrapolation Methods
VI.6 Quasilinear Problems
Chapter VII. Differential-Algebraic Equations of Higher Index
VII.1 The Index and Various Examples
VII.2 Index Reduction Methods
VII.3 Multistep Methods for Index 2 DAE
VII.4 Runge-Kutta Methods for Index 2 DAE
VII.5 Order Conditions for Index 2 DAE
VII.6 Half-Explicit Methods for Index 2 Systems
VII.7 Computation of Multibody Mechanisms
VII.8 Symplectic Methods for constrained Hamiltonian Systems
Appendix. Fortran Codes
Bibliography
Symbol Index
Subject Index
