Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations

• Main Authors: Zainuddin, Nooraini, Ibrahim, Zarina Bibi, Othman, Khairil Iskandar, Suleiman, Mohamed
• Format: Article
• Language: English
• Published: Faculty of Science, Chiang Mai University 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/55533/1/Direct%20fifth%20order%20block%20backward%20differentiation%20formulas%20for%20solving%20second%20order%20.pdf; http://psasir.upm.edu.my/id/eprint/55533/; http://epg.science.cmu.ac.th/ejournal/

In this paper, a new fifth order Direct Block Backward Differentiation Formula (5-DBBDF) for solving second order stiff ordinary differential equations (ODEs) is presented. Five backwards steps are used to generate the coefficients of the 5-DBBDF. This method approximates the solutions at two points concurrently by using fixed step size and solved the second order ODEs directly without reducing the ODEs to a system of first order. Numerical results on some standard problems found in the literature are presented to validate the accuracy of the proposed method.