A Special Class of Multistep Runge-Kutta Methods with Extended Real Stability Interval

摘要

A special class of k-step Runge-Kutta methods is investigated which is generated by nonlinear Chebyshev iteration (Richardson iteration) of an implicit linear multistep method. By terminating the iteration process after m iterations, a family of the k-step, m-stage Runge-Kutta method is obtained whose real stability interval can be derived for general values of k and m by a special application of the boundary locus method. The real stability boundary is maximized by choosing suitable values for the coefficients in the generating k-step method. The considerations are mainly restricted to second order methods. Examples are given for k = 1,2,3, and 4, and numerical experiments are reported with a nonlinear parabolic initial boundary value problem.