Generalized two-step hybrid block method with one off-step point for solving second order ordinary differential equations directly

• Main Authors: Mansor, Kamarun Hizam, Omar, Zurni, Rohni, AM
• Format: Article
• Published: JARDCS 2018
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://repo.uum.edu.my/27942/; https://www.jardcs.org/backissues/abstract.php?archiveid=5938
• Institution: Universiti Utara Malaysia

This paper proposes a new two-step hybrid block method with one generalized off-step point within each step to find the direct solution of second order ordinary differential equation. In deriving this method, a power series is adopted as an approximate solution and interpolated at points while its second derivatives collocated at all points in the given interval to obtain the main continuous scheme. This method generates the non-overlapping starting values using Taylor series. The analysis of the method such as order, zero stability, consistency and convergence is also discussed. The developed method was then compared with the existing methods in terms of accuracy and the results suggest that this method can be served as a viable alternative methods to solve directly initial value problems of second order ordinary differential equations.