Stiff systems of ordinary differential equations (ODEs) arise frequently in several areas of applied mathematics, science, and engineering, and their numerical integration requires methods with strong stability characteristics. In this paper, a block extended backward differentiation formula (BEBDF) with a stability control parameter is developed for the numerical solution of stiff systems of ODEs. The proposed method is constructed within the framework of block multistep methods, allowing the simultaneous computation of solution values at several grid points. A free parameter $\rho$ is incorporated into the formulation of the method to regulate and improve its stability behavior. The presen... More >

In this paper, we present a modified three-point superclass of Block Backward Differentiation Formula (BBDF) for the efficient numerical solution of stiff systems of ordinary differential equations (ODEs). The principal enhancement of this work is a structural modification of the classical BBDF that forms a new parameterized superclass of methods, leading to improved stability and reduced error constants compared with the standard three-point BBDFs. The proposed scheme is formulated as a fully implicit block method capable of simultaneously producing three solution approximations within each integration step. A detailed theoretical analysis is conducted to establish the order of accuracy, co... More >