Errors of linear multistep methods and Runge-Kutta methods for singular perturbation problems with delays

This paper is concerned with the error analysis of linear multistep methods and Runge-Kutta methods applied to some classes of one-parameter stiff singularly perturbed problems with delays. We derive the global error estimates of A(α)-stable linear multistep methods and algebraically and diagonally stable Runge-Kutta methods with Lagrange interpolation procedure. Numerical experiments confirm our theoretical analysis.