This paper investigates iterated Multistep Runge-Kutta methods of Radau type as a class of explicit methods suitable for parallel implementation. Using the idea of van der Houwen and Sommeijer 18], the method is designed in such a way that the right-hand side evaluations can be computed in parallel. We use stepsize control and variable order based on iterated approximation of the solution. A co...

This paper is concerned with the stability of rational one-step approximations of C0 semigroups. Particular emphasis is laid on long-term stability bounds. The analysis is based on a general Banach space framework and allows variable stepsize sequences. Under reasonable assumptions on the stepsize sequence, asymptotic stability bounds for general C0 semigroups are derived. The bounds are typica...

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

The development of a Sundman-type time-transformation for reversible variable stepsize integration of few-body problems is discussed. While a time-transformation based on minimum particle separation is suitable if the collisions only occur pairwise and isolated in time, the control of stepsize is typically much more diicult for a three-body close approach. Nonetheless, we nd that a suitable cho...

Time-stepping methods that guarantee to avoid spurious fixed points are said to be regular. For fixed stepsize Runge-Kutta formulas, this concept has been well studied. Here, the theory of regularity is extended to the case of embedded Runge-Kutta pairs used in variable stepsize mode with local error control. First, the limiting case of a zero error tolerance is considered. A recursive regulari...

The development of a Sundman-type time-transformation for reversible variable stepsize integration of few-body problems is discussed. While a time-transformation based on minimum particle separation is suitable if the collisions only occur pairwise and isolated in time, the control of stepsize is typically much more diicult for a three-body close approach. Nonetheless, we nd that a suitable cho...

We propose two low complexity adaptive step-size mechanisms based on the normalised orthogonal gradient algorithm for frequency-domain equalisation in orthogonal frequency division multiplexing (OFDM) systems. These algorithms are derived from employing a mixed-subcarrier exponentially weighted least squares criterion. Two low complexity adaptive stepsize approaches are investigated by exploiti...

It has recently been observed that with appropriate stepsize normalization, the convergence speed of the constant modulus (CM) algorithm can be dramatically improved. In this correspondence, it is shown that if a different normalization strategy is used, one that takes into account the finite alphabet structure of the signals, a standard normalized version of the decision directed equalizer (DD...

This paper presents the convergence analysis result of the discrete cosine transform-least-mean-square (DCT-LMS) adaptive "ltering algorithm which is based on a well-known interpretation of the variable stepsize algorithm. The time-varying stepsize of the DCT-LMS algorithm is implemented by the modi"ed power estimator to redistribute the spread power after the DCT. The performance analysis is c...