AUTHOREA
Log in
Sign Up
Browse Preprints
LOG IN
SIGN UP
Essential Site Maintenance
: Authorea-powered sites will be updated circa 15:00-17:00 Eastern on Tuesday 5 November.
There should be no interruption to normal services, but please contact us at
[email protected]
in case you face any issues.
Francesca Mazzia
Public Documents
1
An adaptive optimized Runge-Kutta-Nyström method for second-order IVPs
Mufutau Ajani Rufai
and 2 more
February 20, 2022
This research paper is concerned with developing, analyzing, and implementing an adaptive optimized one-step block Nyström method for solving second-order initial value problems of ODEs and time-dependent partial differential equations. The new technique is developed through a collocation method with a new approach for selecting the collocation points. An embedding-like procedure is used to estimate the error of the proposed optimized method. The current approach has produced approximate solutions to real-world oscillatory, periodic and stiff application problems. The numerical experiments demonstrate that the introduced error estimation and stepsize control strategy presented in this manuscript has produced a good performance compared with some of the other existing numerical methods.