Citation
Mohd Ijam, Hazizah and Ibrahim, Zarina Bibi
(2019)
Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations.
Symmetry, 11 (11).
art. no. 1342.
pp. 1-18.
ISSN 2073-8994
Abstract
This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinary Differential Equations (ODEs) to achieve the research objective. The selection of ρ for optimal stability properties in terms of zero stability, absolute stability, error constant and convergence are discussed. In the diagonally implicit formula that uses a lower triangular matrix with identical diagonal entries, allowing a maximum of one lower-upper (LU) decomposition per integration stage to be performed will result in substantial computing benefits to the user. The numerical results and plots of accuracy indicate that the ρ -DIBBDF method performs better than the existing fully and diagonally Block Backward Differentiation Formula (BBDF) methods.
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