Multivalue-multistage method for second-order ODEs

• Main Authors: Ismail, Siti Ainathon, Rabiei, Faranak
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/57327/1/Multivalue-multistage%20method%20for%20second-order%20ODEs.pdf; http://psasir.upm.edu.my/id/eprint/57327/
• Institution: Universiti Putra Malaysia

The aim of this paper is to generate the needed framework to develop order conditions for second-order Ordinary Differential Equations (ODEs) by class of multivalue-multistage Nystrom method. A general approach to study the order conditions of the methods for solving second-order initial value problems is investigated. Our investigation will be carried out by adapting the theory of Nystrom-series and using the sets of second order rooted trees for solving second-order ODEs which leads to a general set of order conditions. In this paper the method of order three using constant step-size algorithm is derived. The stability region of method is also proposed.