Solving ordinary differential equations. I, Nonstiff problems
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Cham :
Springer International publishing
[20..].
Cham : Springer Nature |
| Édition: | 2nd revised edition. |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Variante du titre: | Nonstiff problems |
| Edition sous un autre format: | • Solving ordinary differential equations, I, Nonstiff problems, E. Hairer, S.P. Nørsett, G. Wanner, 2nd revised edition, corrected 3rd printing, Berlin, Springer, 2008, 1 vol. (XV-528 p.), Springer series in computational mathematics, 978-3-540-56670-0 |
Table des matières:
- Chapter I, Classical mathematical theory
- Chapter II, Runge-Kutta and extrapolation methods
- Chapter III, Multistep methods and general linear methods
- 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
- 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
- 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