منابع مشابه
Long-Term Stability of Symmetric Partitioned Linear Multistep Methods
Long-time integration of Hamiltonian systems is an important issue in many applications – for example the planetary motion in astronomy or simulations in molecular dynamics. Symplectic and symmetric one-step methods are known to have favorable numerical features like near energy preservation over long times and at most linear error growth for nearly integrable systems. This work studies the sui...
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page 1 Linear Multistep Methods Note: The authoritative reference for the material on convergence is the book by Peter Henrici, Discrete Variable Methods in Ordinary Differential Equations , Wiley, 1962. The best reference on absolute stability is the book by Jack Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, 1991. We consider the Initial Value Problem (IVP) y′ = f(x, y),...
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We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have been used as higher-order initial value problem solvers for over a century. Fur...
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A method of choice for the long-time integration of constrained Hamiltonians systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitraril...
متن کاملMonotonicity-Preserving Linear Multistep Methods
In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total variation bounded (TVB) property. In the analysis the multistep methods are considered in combination with suitable starting proc...
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2006
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-006-0066-z