Results 101 to 110 of about 240 (144)
Nordsieck methods on nonuniform grids: Stability and order reduction phenomenon
Mathematics and Computers in Simulation, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gennady Yu. Kulikov, Sergey Shindin
openalex +3 more sources
Applied Mathematics and Computation, 2006 This paper is the third in a sequence of papers by the authors on maximum polynomial degree \((k,p)\) Nordsieck-Gear methods for non-stiff ordinary differential equations. The particular features of this paper are that two conjectures from the earlier work are proved and this leads to proofs of convergence and order for the \((k,1)\) method.
Roy Danchick, M. L. Juncosa
openalex +3 more sources
Starting in maximum-polynomial-degree Nordsieck-Gear methods
Applied Mathematics and Computation, 1977 The intent of this paper is to show that the Nordsieck-Gear methods with maximum polynomial degree k+1, first described in [1], admit of matched starting methods which are exact for all polynomials of degree =
Roy Danchick, David A. Pope
openalex +3 more sources
Implementation of Nordsieck second derivative methods for stiff ODEs
Applied Numerical Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali Abdi, Gholamreza Hojjati
openalex +3 more sources
Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs
Computational and Applied Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Batoul Behzad +2 more
openalex +3 more sources
XXVI. A covariant formulation of the Block-Nordsieck method
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1951 Summary The results of the Bloch-Nordsieck method are derived in a covariant manner, based on a covariant form of the commutation-relations in momentum space.
Walter Thirring, B. Touschek
openalex +2 more sources
Nordsieck representation of two-step Runge–Kutta methods for ordinary differential equations
Applied Numerical Mathematics, 2004 Two-step Runge-Kutta methods are a generalization of classical one-step methods, where each integration step reuses quantities computed in the previous step. Although they can attain higher accuracy for a given number of function evaluations than for standard Runge-Kutta methods, they are less convenient to implement with variable stepsize. The authors
Z. Bartoszewski, Z. Jackiewicz
openalex +3 more sources
Solving the order reduction phenomenon in variable step size quasi-consistent Nordsieck methods
Computational Mathematics and Mathematical Physics, 2012 Summary: The phenomenon is studied of reducing the order of convergence by one in some classes of variable step size Nordsieck formulas as applied to the solution of the initial value problem for a first-order ordinary differential equation. This phenomenon is caused by the fact that the convergence of fixed step size Nordsieck methods requires weaker ...
Gennady Yu. Kulikov
openalex +3 more sources
On The Stability of Variable Stepsize Adams Methods in Nordsieck Form
, 1987 The aim of our paper is to show that the stability of Adams methods can be ascertained under weaker assumptions than the ones given in [5] and [13]. In particular it is proved that (k+1)-value Adams methods remain stable if there exists a fixed p ≥ 0, so that after consecutive arbitrary stepsizes whose number is ≤p, there are at least k-1 steps of ...
M. Calvo, F.J. Lisbona, J.I. Montijano
openalex +2 more sources
STARTING IN MAXIMUM POLYNOMIAL DEGREE NORDSIECK-GEAR METHODS
, 1975 Roy Danchick
openalex +2 more sources