Embedded Pairs of Explicit ARKN Methods for the Numerical Integration of Perturbed Oscillators

Article type: Research Article

Authors: Franco, J.M.^;

Affiliations: Departamento de Matemática Aplicada, C.P.S. de Ingeniería, Universidad de Zaragoza, María de Luna 3, 50015 Zaragoza, Spain

Note: [1] E-mail: [email protected].

Abstract: Two new embedded pairs of explicit RKN methods specially adapted to the numerical integration of perturbed oscillators are obtained. These pairs depend upon a parameter ν = ωh>0 (h is the integration step and ω is the frequency), and they have four stages and algebraic orders four and three. The numerical experiments carried out show that the new pairs are very competitive when they are compared with a high quality code as DOPRI5.

Keywords: Adapted RKN methods, embedded pairs, oscillatory problems

Keywords: 65L05, 65L06

DOI: 10.3233/JCM-2003-3305

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 3, pp. 415-424, 2003