Numerical Initial Value Problems in Ordinary Differential EquationsPrentice-Hall, 1971 - 253 Seiten Introduction -- Higher order one-step methods -- Systems of equations and equations of order greater than one -- Convergence, error bounds, and error estimates for one-step methods -- The choice of step size and order -- Extrapolation methods -- Multivalue or multistep methods - introduction -- General multistep methods, order and stability -- Multivalue methods -- Existence, convergence, and error estimates for multivalue methods -- Special methods for special problems -- Choosing a method. |
Inhalt
2 | 25 |
Systems of Equations | 45 |
Convergence Error Bounds | 52 |
Urheberrecht | |
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Häufige Begriffe und Wortgruppen
A-stable a₁ absolute stability accuracy Adams Adams-Bashforth method approximation C₁ Chapter coefficients components computed constant convergence corrector iteration defined derivatives df/dy diagonal differential equation eigenvalues elements error bounds estimate Euler method example extrapolation formula fourth order function evaluations given h₁ Hence hf(y higher order equations implicit initial value problem initial values integrated k-step methods k₁ KFLAG LEMMA linear Lipschitz condition matrix maximum order methods of order multistep methods multivalue methods nonzero normal form numerical solution one-step methods order method parameters Pascal matrix Pascal triangle perturbations predictor proof pth order equations q-root result root condition root of p(5 round-off errors Runge-Kutta method second order solved stable methods starting values stiff differential equations stiff equations stiffly stable SUBROUTINE Table Taylor's series Theorem trapezoidal rule truncation error unit circle vector y₁ Yn+1 zero β₁ Уп Уп+1