Solving ordinary differential equations : I : Nonstiff problems

Solving ordinary differential equations : I Nonstiff problems

Détails bibliographiques
Auteurs principaux : Hairer Ernst (Auteur), Nørsett Syvert Paul (Auteur), Wanner Gerhard (Auteur)
Format : Livre
Langue : anglais
Titre complet : Solving ordinary differential equations. I, Nonstiff problems / E. Hairer, S.P. Nørsett, G. Wanner
Édition : 2nd revised edition, corrected 3rd printing
Publié : Berlin, Heidelberg, New York [etc.] : Springer , 2008, cop. 1993
Description matérielle : 1 vol. (XV-528 p.)
Collection : Springer series in computational mathematics ; 8
Sujets :
Équations différentielles > Solutions numériques
Runge-Kutta, Méthode de
Problèmes aux valeurs initiales
Calculs numériques
Documents associés : Nonstiff problems: Solving ordinary differential equations
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200 1 |a Solving ordinary differential equations  |h I  |i Nonstiff problems  |f E. Hairer, S.P. Nørsett, G. Wanner 
205 |a 2nd revised edition, corrected 3rd printing 
210 |a Berlin  |a Heidelberg  |a New York [etc.]  |c Springer  |d 2008, cop. 1993 
215 |a 1 vol. (XV-528 p.)  |c ill.  |d 24 cm 
225 2 |a Springer series in computational mathematics  |v 8 
305 |a Autre tirage : 2009 (br.) 
320 |a Bibliogr. p. [491]-519. Index 
359 2 |b Chapter I, Classical mathematical theory  |c I.1, Terminology  |c I.2, The oldest differential equations  |c I.3, Elementary integration methods  |c I.4, Linear differential equations  |c I.5, Equations with weak singularities  |c I.6, Systems of equations  |c I.7, A general existence theorem  |c I.8, Existence theory using iteration methods and Taylor series  |c I.9, Existence theory for systems of equations  |c I.10, Differential inequalities  |c I.11, Systems of linear differential equations  |c I.12, Systems with constant coefficients  |c I.13, Stability  |c I.14, Derivatives with respect to parameters and initial values  |c I.15, Boundary value and eigenvalue problems  |c I.16, Periodic solutions, limit cycles, strange attractors  |b Chapter II, Runge-Kutta and extrapolation methods  |c II.1, The first Runge-Kutta methods  |c II.2, Order conditions for Runge-Kutta methods  |c II.3, Error estimation and convergence for RK methods  |c II.4, Practical error estimation and step size selection  |c II.5, Explicit Runge-Kutta methods of higher order  |c II.6, Dense output, discontinuities, derivatives  |c II.7, Implicit Runge-Kutta methods  |c II.8, Asymptotic expansion of the global error  |c II.9, Extrapolation methods  |c II.10, Numerical comparisons  |c II.11, Parallel methods  |c II.12, Composition of B-series  |c II.13, Higher derivative methods  |c II.14, Numerical methods for second order differential equations  |c II.15, P-series partitioned differential equations  |c II.16, Sympletic integration methods  |c II.17, Delay differential methods  |b Chapter III, Multistep methods and general linear methods  |c III.1, Classical linear multistep formulas  |c III.2, Local error and order conditions  |c III.3, Stability and the first Dahlquist barrier  |c III.4, Convergence and multistep methods  |c III.5, variable step size multistep methods  |c III.6, Nordsieck methods  |c III.7, Implementation and numerical comparisons  |c III.8, General linear methods  |c III. 9, Asymptotic expansion of the global error  |c III.10, Multistep methods for second order differential equations  |c Appendix, Fortran codes 
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