Strong Stability Preserving General Linear Methods with Runge–Kutta Stability

Abstract

We investigate strong stability preserving (SSP) general linear methods (GLMs) for systems of ordinary differential equations. Such methods are obtained by the solution of the minimization problems with nonlinear inequality constrains, corresponding to the SSP property of these methods, and equality constrains, corresponding to order and stage order conditions. These minimization problems were solved by the sequential quadratic programming algorithm implemented in MATLAB $$^{\circledR }$$ subroutine fmincon.m starting with many random guesses. Examples of transformed SSP GLMs of order $$p = 1, 2, 3$$ , and 4, and stage order $$q = p$$ have been determined, and suitable starting and finishing procedures have been constructed. The numerical experiments performed on a set of test problems have shown that transformed SSP GLMs constructed in this paper are more accurate than transformed SSP DIMSIMs and SSP Runge–Kutta methods of the same order.