Resumen de A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations

Higinio Ramos Calle , Jesús Vigo-Aguiar

• In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge-Kutta method having stage order four. The method thus obtained have good properties relatives to stability including an unbounded stability domain and large a-value concerning A(a)-stability. A strategy for changing the step size, based on a pair of methods in a similar way to the embedding pair in the Runge-Kutta schemes, is presented. The numerical examples reveals that this method is very promising when it is used for solving stiff initial-value problems.