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
  • Chapter I, Classical mathematical theory
  • I.1, Terminology
  • I.2, The oldest differential equations
  • I.3, Elementary integration methods
  • I.4, Linear differential equations
  • I.5, Equations with weak singularities
  • I.6, Systems of equations
  • I.7, A general existence theorem
  • I.8, Existence theory using iteration methods and Taylor series
  • I.9, Existence theory for systems of equations
  • I.10, Differential inequalities
  • I.11, Systems of linear differential equations
  • I.12, Systems with constant coefficients
  • I.13, Stability
  • I.14, Derivatives with respect to parameters and initial values
  • I.15, Boundary value and eigenvalue problems
  • I.16, Periodic solutions, limit cycles, strange attractors
  • Chapter II, Runge-Kutta and extrapolation methods
  • II.1, The first Runge-Kutta methods
  • II.2, Order conditions for Runge-Kutta methods
  • II.3, Error estimation and convergence for RK methods
  • II.4, Practical error estimation and step size selection
  • II.5, Explicit Runge-Kutta methods of higher order
  • II.6, Dense output, discontinuities, derivatives
  • II.7, Implicit Runge-Kutta methods
  • II.8, Asymptotic expansion of the global error
  • II.9, Extrapolation methods
  • II.10, Numerical comparisons
  • II.11, Parallel methods
  • II.12, Composition of B-series
  • II.13, Higher derivative methods
  • II.14, Numerical methods for second order differential equations
  • II.15, P-series partitioned differential equations
  • II.16, Sympletic integration methods
  • II.17, Delay differential methods
  • Chapter III, Multistep methods and general linear methods
  • III.1, Classical linear multistep formulas
  • III.2, Local error and order conditions
  • III.3, Stability and the first Dahlquist barrier
  • III.4, Convergence and multistep methods
  • III.5, variable step size multistep methods
  • III.6, Nordsieck methods
  • III.7, Implementation and numerical comparisons
  • III.8, General linear methods
  • III. 9, Asymptotic expansion of the global error
  • III.10, Multistep methods for second order differential equations
  • Appendix, Fortran codes