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- Publications
- Influence

On Error Estimates for Waveform Relaxation Methods for Delay-Differential Equations

- Z. Bartoszewski, M. Kwapisz
- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 1 July 2000

In this paper the problem of delay-dependent error estimates for waveform relaxation methods applied to systems of delay-differential equations is discussed. Under suitable conditions imposed on the… Expand

Delay dependent estimates for waveform relaxation methods for neutral differential-functional systems

- Z. Bartoszewski, M. Kwapisz
- Mathematics
- 1 December 2004

In this paper, the problem of delay dependent error estimates for waveform relaxation methods applied to Volterra type systems of functional-differential equations of neutral type including systems… Expand

Construction of two-step Runge-Kutta methods of high order for ordinary differential equations

- Z. Bartoszewski, Z. Jackiewicz
- Computer Science, Mathematics
- Numerical Algorithms
- 1 September 1998

The construction of two-step Runge-Kutta methods of order p and stage order q=p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute… Expand

On the Convergence of Waveform Relaxation Methods for Differential-Functional Systems of Equations

- Z. Bartoszewski, M. Kwapisz
- Mathematics
- 15 July 1999

In this paper the convergence of a waveform relaxation method applied to an initial value problem for the Volterra functional-differential system is discussed. It is shown that the method is… Expand

A new approach to numerical solution of fixed-point problems and its application to delay differential equations

- Z. Bartoszewski
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 February 2010

In this paper we consider a certain approximation of fixed-points of a continuous operator A mapping the metric space into itself by means of finite dimensional @e(h)-fixed-points of A. These finite… Expand

Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations

- Z. Bartoszewski, Z. Jackiewicz
- Mathematics
- 1 May 2005

We describe a new representation of explicit two-step Runge-Kutta methods for ordinary differential equations. This representation makes it possible for the accurate and reliable estimation of local… Expand

On the convergence of iterative methods for general differential--algebraic systems

- Z. Bartoszewski, T. Jankowski, M. Kwapisz
- Mathematics
- 15 August 2004

In this paper the existence and uniqueness of solutions to quite general classes of integro-algebraic systems and differential-algebraic systems are investigated. The convergence of different… Expand

Derivation of continuous explicit two-step Runge-Kutta methods of order three

- Z. Bartoszewski, Z. Jackiewicz
- Mathematics
- 20 August 2007

We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and… Expand

Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations

- Z. Bartoszewski, Z. Jackiewicz
- Mathematics
- 1 October 2008

It is shown that any A-stable two-step Runge-Kutta method of order p@? and stage order q=p@? for ordinary differential equations can be extended to the P-stable method of uniform order p=p@? for… Expand

Construction of stiffly accurate Two-Step Runge-Kutta Methods of order three and their continuous extensions using Nordsieck representation

- Z. Bartoszewski, H. Podhaisky, R. Weiner
- Mathematics
- 2006

We describe a construction of implicit two–step Runge–Kutta methods for ordinary differential equations in Nordsieck form and their continuous extensions. This representation allows accurate and… Expand

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