Solving Ordinary Differential Equations I: Nonstiff ProblemsSpringer Science & Business Media, 2008年4月16日 - 528 頁 This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included. |
內容
I | 2 |
Clairaut | 9 |
I | 16 |
Nonlinear Equations | 23 |
Exercises | 34 |
Exercises | 43 |
Methods | 44 |
9 | 51 |
6 | 188 |
Exercises | 223 |
Comparisons | 244 |
A Stretched Error Estimator for DOP853 | 254 |
BSeries | 266 |
Methods | 275 |
Equations | 283 |
PSeries | 298 |
Exercises | 55 |
The RouthHurwitz Criterion | 81 |
Stability of Nonlinear Systems | 87 |
Problems | 105 |
Strange Attractors | 120 |
Exercises | 126 |
RungeKutta and Extrapolation Methods | 129 |
Optimal Formulas | 139 |
The Derivatives of the True Solution | 145 |
Exercises | 154 |
4 | 164 |
Numerical Experiments | 170 |
Higher Order Processes | 179 |
Order Conditions for Partitioned RungeKutta Methods | 307 |
Exercises | 352 |
Numerical Experiment | 361 |
The Peano Kernel of a Multistep Method | 375 |
Equivalence with Multistep Methods | 412 |
Order Conditions for General Linear Methods | 436 |
Exercises | 445 |
Weakly Stable Methods | 454 |
Appendix Fortran Codes | 475 |
| 491 | |
| 521 | |
其他版本 - 查看全部
常見字詞
4th order Adams methods algorithm applied approximation asymptotic expansion b₁ b₂ coefficients collocation collocation method compute consider convergence corresponding defined Definition denote dense output derivatives differential equation DOPRI5 Dormand & Prince eigenvalues equivalent error estimate Euler Euler method exact solution example Exercise explicit Adams extrapolation Fehlberg formula function evaluations given global error Hamiltonian Hermite interpolation implicit implies initial values integration interpolation IWORK Kutta Lemma limit cycle linear matrix method of order multistep method norm numerical solution Nyström methods obtain ODEX order conditions order methods ordinary differential equations P-trees P₁ parameters Poincar´e polynomial problem Proof quadrature result Richardson extrapolation root Runge-Kutta method satisfies Section sequence shows solve stability SUBROUTINE symplectic t₁ Table Taylor series Theorem tion trees of order vector xend Xn+1 y₁ Yn+1 zero მყ
熱門章節
第 510 頁 - One-step methods of Hermite type for numerical integration of stiff systems, BIT 14 (1974) 63-77.
第 493 頁 - Analysis problematis antehac propositi, de inventione lineae descensus a corpore gravi percurrendae uniformiter, sic ut temporibus aequalibus aequales altitudines emetiatur: et alterius cujusdam Problematis Propositio, in: Acta eruditorum, Mai 1690, S.