Direct Fifth Order Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations
Nooraini Zainuddin [b,c], Zarina Bibi Ibrahim*[a,b], Khairil Iskandar Othman [d] and Mohamed Suleiman [a,b]* Author for corresponding; e-mail address: zarinabb@upm.edu.my
Volume: Vol.43 No.5 (OCTOBER 2016)
Research Article
DOI:
Received: 12 November 2014, Revised: -, Accepted: 12 April 2015, Published: -
Citation: Zainuddin N., Ibrahim Z.B., Othman K.I. and Suleiman M., Direct Fifth Order Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations, Chiang Mai Journal of Science, 2016; 43(5): 1171-1181.
Abstract
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.