Result: Starting algorithms for low stage order RKN methods
Title:
Starting algorithms for low stage order RKN methods
Authors:
Source:
Journal of Computational and Applied Mathematics. 140:345-367
Publisher Information:
Elsevier BV, 2002.
Publication Year:
2002
Subject Terms:
Applied Mathematics, Numerical computation of solutions to systems of equations, order conditions, Nyström methods, starting algorithms, Starting algorithms, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, iterative schemes, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Iterative schemes, Computational Mathematics, nonlinear systems, 0101 mathematics
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0377-0427
DOI:
10.1016/s0377-0427(01)00479-4
Access URL:
https://zbmath.org/1758436
https://doi.org/10.1016/s0377-0427(01)00479-4
https://ui.adsabs.harvard.edu/abs/2002JCoAM.140..345G/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042701004794
https://dl.acm.org/doi/10.1016/S0377-0427%2801%2900479-4
https://www.sciencedirect.com/science/article/pii/S0377042701004794
https://doi.org/10.1016/s0377-0427(01)00479-4
https://ui.adsabs.harvard.edu/abs/2002JCoAM.140..345G/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042701004794
https://dl.acm.org/doi/10.1016/S0377-0427%2801%2900479-4
https://www.sciencedirect.com/science/article/pii/S0377042701004794
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....bbae953e1036d44bba51185235754fbb
Database:
OpenAIRE
Further Information
While solving second-order differential equations with Runge-Kutta-Nyström (RNK) methods, usually the computational effort is dominated by the cost of solving nonlinear systems. For this reason, it is necessary to have good starting values to begin the iterations. The authors consider a type of starting algorithms without additional computational cost. They study the general order conditions and observe that the maximum order is achieved when the Runge-Kutta-Nyström method satisfies some simplifying assumptions.