Stability analysis of a diagonally implicit scheme of block backward differentiation formula for stiff pharmacokinetics models

In this paper, we analyze the criteria for the stability of a method suited to the ordinary differential equations models. The relevant proof that the method satisfies the condition of stiff stability is also provided. The aim of this paper is therefore to construct an efficient two-point block method based on backward differentiation formula which is A-stable and converged. The new diagonally implicit scheme is formulated to approximate the solution of the pharmacokinetics models. By implementing the algorithm, the numerical solution to the models is compared with a few existing methods and established stiff solvers. It yields significant advantages when the diagonally implicit method with a lower triangular matrix and identical diagonal elements is considered. The formula is designed in such a way that it permits a maximum of one LU decomposition for each integration stage.