On the Stability Properties of Brown's Multistep Multiderivative Methods.
On the Uniform Power-Boundedness of a Family of Matrices and the applications to One-Leg and Linear Multistep Methods.
On the unique solvability of the Runge-Kutta equations.
On the Zero Stability of the Variable Order Variable Stepsize BDF-Formulas.
On total truncation error estimation for the one-step method
In this paper the author establishes estimation of the total truncation error after steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.
On Transformations of Graded Matrices, with Applications to Stiff ODE's.
One parameter family of linear difference equations and the stability problem for the numerical solution of ODEs.
One-dimensional adaptive grid generation.
One-step and Extrapolation Methods for Differential-Algebraic Systems.
One-step methods for neutral delay-differential equations with state dependent delays
One-Step Methods of Any Order for Ordinary Differential Equations with Discontinuous Right-Hand Sides.
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...
Optimal snapshot location for computing POD basis functions
The construction of reduced order models for dynamical systems using proper orthogonal decomposition (POD) is based on the information contained in so-called snapshots. These provide the spatial distribution of the dynamical system at discrete time instances. This work is devoted to optimizing the choice of these time instances in such a manner that the error between the POD-solution and the trajectory of the dynamical system is minimized. First and second order optimality systems are given. Numerical...
Optimale Verfahren zur numerischen Integration von Anfangswertproblemen.
Optimally stable fifth-order integration methods: A numerical approach.
Optimum error estimates for finite-difference methods
Order and Stepsize Control in Extrapolation Methods
Order Conditions for Numerical Methods for Partitioned Ordinary Differential Equations.
Order conditions for partitioned Runge-Kutta methods
We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations.
Order Conditions for Rosenbrock Type Methods.