Reyes, José Antonio, García-Alonso, Fernando
Computational series and multistep methods to integrate forced and damped stiff oscillators
The Open Applied Mathematics Journal. 2012, 6: 9-22. doi:10.2174/1874114201206010009
URI: http://hdl.handle.net/10045/36060
DOI: 10.2174/1874114201206010009
ISSN: 1874-1142
Abstract: 
In a first part, this article presents the adaptation of Scheifele functions to forced and damped oscillators, designing a series method based on these, which integrates the non perturbed problem with no truncation error. This method is highly accurate, however it is difficult to adapt to each specific problem. In order to overcome this difficulty, in a second part, we describe the transformation of the series method to a multistep scheme. Explicit and implicit methods are formulated and combine to create a predictor-corrector method, which precisely integrates the homogenous problem. The computational algorithm is developed and the results obtained are contrasted by the series method and by the multistep algorithm with other known integrators.
Keywords:Numerical solutions of oscillators, Highly accurate solutions, Highly oscillatory problems, Stiff problems, Multistep algorithms, computational algorithms
Bentham Open
info:eu-repo/semantics/article