Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations

Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman

Abstract:

In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.

Keywords: Backward Differentiation Formula, block, secondorder.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334566

References:

[1] F. T. Krogh, A Variable Step, variable order multistep method for the numerical solution of ordinary differential equations, Proceedings of the IFIP Congress in Information Processing , 1968, pp. 194-199.
[2] M.B. Suleiman, "Generalized Multistep Adams and Backward Differentiation Methods for the solution of stiff and non-stiff ordinary differential equations," PhD. dissertation, Manchester Univ., 1979.