Modified order and stepsize strategies in Adams codes

Implementing Adams Methods with Preassigned Stepsize Ratios

Runge-Kutta and Adams methods are the most popular codes to solve numerically nonstiff ODEs. The Adams methods are useful to reduce the number of function calls, but they usually require more CPU time than the Runge-Kutta methods. In this work we develop a numerical study of a variable step length Adams implementation, which can only take preassigned step-size ratios. Our aim is the reduction o...

Experiments in stepsize control for Adams linear multistep methods

Switching Stepsize Strategies for SQP

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...

Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes

The potential for adaptive explicit Runge–Kutta (ERK) codes to produce global errors that decrease linearly as a function of the error tolerance is studied. It is shown that this desirable property may not hold, in general, if the leading term of the locally computed error estimate passes through zero. However, it is also shown that certain methods are insensitive to a vanishing leading term. M...

Analysis of Stepsize Selection Schemes for Runge - Kutta Codes

Conditions on Runge-Kutta algorithms can be obtained which ensure smooth stepsize selection when stability of the algorithm is restricting the stepsize. Some recently derived results are shown to hold for a more general test problem.