Stiff systems of ordinary differential equations (ODEs) arise frequently in science, engineering, and applied mathematics, and their numerical solutions require methods with strong stability properties to avoid severe step-size restrictions. This motivates the development of efficient and stable numerical schemes tailored for such problems. In this paper, a fully implicit hybrid block method, termed the Two-Point Superclass Block Backward Differentiation Formula with Off-step Points (2SBBDFO), is proposed for solving stiff ODE systems. The method extends the classical two-point block BDF by incorporating a non-zero coefficient $\beta_{k-1}$, enabling the simultaneous computation of two grid-... More >

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 >