منابع مشابه
Multistep Methods
All of the numerical methods that we have developed for solving initial value problems are onestep methods, because they only use information about the solution at time tn to approximate the solution at time tn+1. As n increases, that means that there are additional values of the solution, at previous times, that could be helpful, but are unused. Multistep methods are time-stepping methods that...
متن کاملLinear Multistep Methods page 1 Linear Multistep Methods
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),...
متن کاملProbabilistic Linear Multistep Methods
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...
متن کاملConstruction of Variable-Stepsize Multistep Formulas
A systematic way of extending a general fixed-stepsize multistep formula to a minimum storage variable-stepsize formula has been discovered that encompasses fixed-coefficient (interpolatory), variable-coefficient (variable step), and fixed leading coefficient as special cases. In particular, it is shown that the " interpolatory" stepsize changing technique of Nordsieck leads to a truly variable...
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: Banach Center Publications
سال: 1984
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-13-1-407-424