Linear Multistep Methods for Integrating Reversible Differential Equations
نویسندگان
چکیده
منابع مشابه
Linear multistep methods for integrating reversible differential equations
This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here, we report on a subset of these methods – the zero-growth methods – that evade these instabilities. ...
متن کاملLinear Multistep Methods for Impulsive Differential Equations
This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and twostep BDFmethod are of order p 0when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the p...
متن کاملLinear Multistep Methods for Volterra Integral and Integro-Differential Equations
In these appendices we present, successively, I conditions for the existence of a unique solution of (1.1) and (1.2); II three tables of coefficients of forward differentiation formulas, and of two common LM formulas for ODEs, viz., backward differentiation formulas and Adams-Moulton formulas; III two lemmas which are needed in: IV proofs of the main results of this paper, as far as they are no...
متن کاملLinear Multistep Methods for Stable Differential Equations y = Ay + B {
The approximation of y=Ay + B't)y +c(t) by linear multistep methods is studied. It is supposed that the matrix A is real symmetric and negative semidefinite, that the multistep method has an interval of absolute stability [—s, 0], and that h2 II A II < s where h is the time step. A priori error bounds are derived which show that the exponential multiplication factor is of the formexp{r;i||B|||„...
متن کاملReversible linear differential equations
Let ∇ be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism σ : Γ → Γ is called a symmetry of ∇ if the pull-back bundle and the pull-back connection can be identified with ∇. We study the symmetries by means of what we call the Fano Group; and, under the hypothesis that ∇ has a unimodular reductive Galois group, we relate the differential Galois group,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Astronomical Journal
سال: 1999
ISSN: 0004-6256
DOI: 10.1086/301057