An accurate continuous hybrid block Method for the Direct Solution of general second initial value problem

• Main Authors: Abdelrahim, Ra`ft, Omar, Zurni, Hijazi, Mohamaad, Alsafi, Firas
• Format: Article
• Language: English
• Published: Medwell journals 2019
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://repo.uum.edu.my/27924/1/JMMS%2013%201%202019%2015%2020.pdf; http://repo.uum.edu.my/27924/; http://doi.org/10.36478/jmmstat.2019.15.20

In this research, a new hybrid block method of order 5 for solving second order Initial Value Problems (IVPs) is determined. One step with 3 off step points is used to generate the coefficients of the new method. This method approximates the solutions of the second order IVPS at xn+1/6, xn+2/6, xn+3/6, xn+1, concurrently by using interpolation and collocation approach with fixed step size. The developed method don’t need to reduce the IVPs to its equivalent system of first order IVPs. The numerical results obtained show that the new method outperforms the existing methods in terms of error.