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On Error Estimates for Waveform Relaxation Methods for Delay-Differential Equations
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 theExpand
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Delay dependent estimates for waveform relaxation methods for neutral differential-functional systems
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 systemsExpand
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Construction of two-step Runge-Kutta methods of high order for ordinary differential equations
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 absoluteExpand
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On the Convergence of Waveform Relaxation Methods for Differential-Functional Systems of Equations
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 isExpand
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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 finiteExpand
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Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
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 localExpand
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On the convergence of iterative methods for general differential--algebraic systems
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 differentExpand
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Derivation of continuous explicit two-step Runge-Kutta methods of order three
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 andExpand
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Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations
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@? forExpand
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Construction of stiffly accurate Two-Step Runge-Kutta Methods of order three and their continuous extensions using Nordsieck representation
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 andExpand
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