Results 21 to 30 of about 14,327,559 (281)
上海师范大学学报. 自然科学版, 2021 This paper is concerned with the asymptotic stability of numerical methods applied to linear differential-algebraic equations. The coefficient matrices of the system are constant rectangular matrices.
SUN Leping
doaj +1 more source
Stability of one-step and linear multistep methods - a matrix technique approach
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We investigate the stability of one-step and linear multistep methods from a new direction. Our aim is to modify the long and technical proof which is consequently omitted in almost every textbook and make it user-friendly.
Miklós Emil Mincsovics
doaj +1 more source
Full linear multistep methods as root-finders [PDF]
Applied Mathematics and Computation, 2018 Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However, used as root-finders, the interpolation points are convergent so that such stability issues are circumvented.
Bart S. van Lith +2 more
openaire +5 more sources
On overcoming Dahlquist’s second barrier for$A$-stable linear multistep methods [PDF]
Iranian Journal of Numerical Analysis and OptimizationDahlquist’s second barrier limits the order of $A$-stable linear multistep methods to at most two, posing significant challenges for achieving higher accuracy in the numerical solution of stiff ordinary differential equations.
G. Hojjati, S. Fazeli, A. Moradi
doaj +1 more source
Estimation of Longest Stability Interval for a Kind of Explicit Linear Multistep Methods
Discrete Dynamics in Nature and Society, 2010 The new explicit linear three-order four-step methods with longest interval of absolute stability are proposed. Some numerical experiments are made for comparing different kinds of linear multistep methods.
Y. Xu, J. J. Zhao
doaj +1 more source
Exponential Multistep Methods for Stiff Delay Differential Equations
Axioms, 2022 Stiff delay differential equations are frequently utilized in practice, but their numerical simulations are difficult due to the complicated interaction between the stiff and delay terms.
Rui Zhan +3 more
doaj +1 more source
Stability analysis of linear multistep methods for delay differential equations
International Journal of Mathematics and Mathematical Sciences, 1986 Stability properties of linear multistep methods for delay differential equations with respect to the test equation y′(t)=ay(λt)+by(t), t≥0 ...
V. L. Bakke, Z. Jackiewicz
doaj +1 more source
Linear Multistep Methods for Functional Differential Equations [PDF]
Mathematics of Computation, 1987 The author discusses linear multistep methods for functional differential equations which are correct for the jumps in the derivatives of the solution. The asymptotic behavior of the global discretization error is discussed as well as the implementation of these methods in predictor- corrector mode with step changing strategy based on the estimation of
openaire +2 more sources
On monotonicity and boundedness properties of linear multistep methods [PDF]
Mathematics of Computation, 2005 In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures.
W. Hundsdorfer (Willem), S.J. Ruuth
openaire +5 more sources
Conjugate-symplecticity of linear multistep methods
, 2008 For the numerical treatment of Hamiltonian differential equations, symplectic integrators are the most suitable choice, and methods that are conjugate to a symplectic integrator share the same good long-time behavior. This note characterises linear multistep methods whose underlying one-step method is conjugate to a symplectic integrator.
Hairer, Ernst
core +3 more sources