This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is ...

Multiple time stepping can be applied to the leapfrog/Stt ormer/Verlet integrator so as to eeect variable stepsize. The strategy maintains the symplecticness, time-reversibility, and second-order accuracy of leapfrog. This method can be applied to pairwise interactions by partitioning them into distance classes and smoothly decomposing the potential energy into the sum of potential energy funct...

This report is devoted to the study and to the comparison of methods for estimation of the local error and for adaptive step-size control when solving the generalised nonlinear Schrodinger equation (GNLSE) in optics by the Interaction Picture (IP) method or by the Symmetric Split-Step (S3F) method. Namely, we propose and study the use of an embedded Runge-Kutta method to solve the nonlinear pro...

There is considerable evidence suggesting that for Hamiltonian systems of ordinary differential equations it is better to use numerical integrators that preserve the symplectic property of the ow of the system, at least for long-time integrations. We present what we believe is a practical way of doing symplectic integration with variable stepsize. Another idea, orthogonal to variable stepsize, ...

An SQP algorithm is presented for solving constrained nonlinear programming problems. The algorithm uses three stepsize strategies in order to achieve global and superlinear convergence. Switching rules are implemented that combine the merits and avoid the drawbacks of the three stepsize strategies. A penalty parameter is determined using an adaptive strategy that aims to achieve sufficient dec...

When the stepsize in Runge-Kutta codes is restricted by stability, an uneven pattern of stepsizes with many step rejections is frequently observed. A modiied strategy is proposed to smooth out this type of behaviour. Several new estimates for the dominant eigenvalue of the Jacobian are derived. It is shown that such estimates can be used, in a strictly controlled way, to improve the stepsize st...

In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval (0, 2) instead of interval (0, (1 + √ 5)/2). As usual, our analysis is established by interpreting this ADMM variant as an instance...

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...

The numerical integration of reversible dynamical systems is considered. A backward analysis for variable stepsize one-step methods is developed, and it is shown that the numerical solution of a symmetric one-step method, implemented with a reversible stepsize strategy, is formally equal to the exact solution of a perturbed differential equation, which again is reversible. This explains geometr...

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...