Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56943", author = "Zarina Bibi Ibrahim and Mohamed Suleiman and Khairil Iskandar Othman", title = "Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations", 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.", volume = "2", number = "4", pages = "259-3", }