Implementing Adams Methods with Preassigned Stepsize Ratios

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

Parallel Adams methods

In the literature, various types of parallel methods for integrating nonsti initial-value problems for rst-order ordinary di erential equation have been proposed. The greater part of them are based on an implicit multistage method in which the implicit relations are solved by the predictor–corrector (or xed point iteration) method. In the predictor–corrector approach the computation of the comp...

Fast convergence pirkn-type pc methods with adams-type predictors

This paper discusses predictor-corrector iteration schemes (PC iteration schemes) based on direct collocation-based Runge-Kutta-Nystr??m corrector methods (RKN corrector methods) for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y??(t)=f(y(t)). Our approach is to regard the well-known parallel-iterated RKN methods (PIRKN methods) as PC...

Chaotic oscillators design with preassigned spectral characteristics

At present, active search for possible chaos applications goes. However to apply dynamical chaos, it is necessary to have signal sources generating chaotic signals. As is known, chaotic oscillators play the role of the sources. Now, there is a large variety of chaotic oscillators which differ from each other by both the structure and elements, and which have various characteristics. On the othe...