New strategy of developing a direct two-step implicit hybrid block method with generalized Two off-step points for third order ordinary differential equations

• Main Authors: Mansor, Kamarun Hizam, Omar, Zurni
• Format: Article
• Language: English
• Published: The Mattingley Publishing Co., Inc. 2018
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://repo.uum.edu.my/27921/1/IJIGS%2012%201%202018%201%20763.pdf; http://repo.uum.edu.my/27921/; http://ijigs.net/archieves/2018/volume-12/issue-01

This paper proposes new strategy in developing a direct two-step implicit hybrid block method with generalized two off-step points for initial value problems (IVPs) of third order ordinary differential equations (ODEs). In this strategy, two off-step points are confined in the second step of two-step interval. The main continuous schemes are obtained through interpolating approximate solutions in the form of power series at three the grid points while its second derivatives are collocated at all the grid points in the interval. The analysis of the method such as order, zero stability, consistency and convergence are also discussed. It was found that the proposed method outperforms the existing methods. Hence, it can be considered as a viable alternative method to solve the thirdorder of IVPs directly.