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

作者：Ramos Higinio^*; Garcia Rubio R

来源：International Journal of Computer Mathematics, 2011, 88(3): 555-577.

DOI：10.1080/00207161003631877

• Runge-Kutta collocation methods
• initial-value problems
• BDF-type methods
• Chebyshev nodes

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(alpha)-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.

• 出版日期2011