The stability problem for linear multistep methods: Old and new results
نویسندگان
چکیده
منابع مشابه
Stability of implicit - explicit linear multistep methods
In many applications, large systems of ordinary di erential equations (ODEs) have to be solved numerically that have both sti and nonsti parts. A popular approach in such cases is to integrate the sti parts implicitly and the nonsti parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linea...
متن کاملConvergence results for linear multistep methods for quasi-singular perturbed problem systems
Stiff behavior occurs in a variety of ODE systems relevant in applications. The notion of stiffness is a phenomenological one, and a stability and error analysis of numerical methods has been based either on simple models or particular problem structures. In particular, stiff initial value problems in standard singular perturbation form are well understood. However, problems of this type exhibi...
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 کاملLong-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...
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: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.10.052