常微分方程的解法Ⅱ

內(nèi)容概要

《常微分方程的解法Ⅱ：剛性與微分代數(shù)問題(第二版)))是關(guān)于剛性微分方程和微分代數(shù)系統(tǒng)(帶約束項的微分方程)的解法。全書共分四章，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(shù)方程及其在約束力學系統(tǒng)中的應用。本書每一章從介紹方法開始，依次討論實際應用、數(shù)值結(jié)果、階和精度的理論分析，線性和非線性穩(wěn)定性、收斂性和漸近展開。剛性問題和微分代數(shù)問題來源于科學計算的各個方面(如物理、化學、生物、控制工程、電網(wǎng)分析及力學系統(tǒng))。本書包含了這些方面的各種應用及計算機程序。    2003年，在澳大利亞的悉尼舉行的ICIAM會議上，本書作者 Ernst Hairer和Gerhard Wanner被授予Peter Henrici獎。

書籍目錄

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-ConvergenceChapter 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 MethodsChapter 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 ProblemsChapter 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 CodesBibliographySymbol IndexSubject Index

圖書封面

圖書標簽Tags

無

評論、評分、閱讀與下載

---

    常微分方程的解法Ⅱ PDF格式下載

---