Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems"Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete. |
Contents
StepControl Stability | 26 |
AaStability | 46 |
Introduction | 53 |
Copyright | |
5 other sections not shown
Other editions - View all
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic ... Ernst Hairer,Gerhard Wanner No preview available - 2010 |
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic ... Ernst Hairer,Gerhard Wanner No preview available - 2004 |
Common terms and phrases
A-stable algebraically stable applied approximation b₁ Burrage c₁ C₂ coefficients collocation methods compute consider convergence Dahlquist defined Definition denote derivatives diagonal differential equation differential-algebraic DOPRI5 eigenvalues error constant estimate Euler method exact solution Exercise explicit extrapolation follows given global error Hairer implicit Euler method implicit Runge-Kutta methods implies initial values Inserting iteration IWORK Jacobian Jeltsch Lemma linear multistep methods linearly implicit Lobatto IIIC LSODE Lubich matrix method of order non-negative nonlinear NSTEP numerical solution O(h³ obtain order conditions order star ordinary differential equations Padé approximations parameters perturbation polynomial proof of Theorem Prove quadrature formula Radau IIA rational function result RK-method root locus Rosenbrock methods Runge-Kutta methods satisfies SDIRK Section stability domain stability function stiff differential equations stiff equations SUBROUTINE t₁ Table trapezoidal rule trees vector y₁ yields Yn+1 z₁ zeros