Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge–Kutta collocation methods

Abstract

The construction of a class of backward differentiation formulae based on intra-step Chebyshev–Gauss–Lobatto nodal points, suitable for the approximate numerical integration of initial-value problems of first-order ordinary differential equations, is presented. Formulae of this new family are A 0-stable and L(α)-stable for any orders, and, particularly, for orders 1 and 2 they are L-stable. Regions of absolute stability and stability measures make this class very promising. We prove that this family of methods may be considered as Runge–Kutta collocation methods where the abscissae are obtained from the Chebyshev–Gauss–Lobatto points.