variable stepsize implementation, initial-value problems, local error estimation, stiff systems, A-stability; L-stability; Local error estimation; Two-step continuous methods; Variable stepsize implementation; Theoretical Computer Science; Computer Science (all); Numerical Analysis; Modeling and Simulation; Applied Mathematics, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, \(L\)-stability, Numerical methods for stiff equations, two-step continuous methods, error estimation, Mesh generation, refinement, and adaptive methods for ordinary differential equations, \(A\)-stability, two-step Runge-Kutta methods, numerical experiments, Stability and convergence of numerical methods for ordinary differential equations, Error bounds for numerical methods for ordinary differential equations