A Class of Explicit Two-Step Runge-Kutta Methods with Enlarged Stability Regions for Parallel Computers

. In this paper we study a class of explicit pseudo two-step Runge-Kutta (EPTRK) methods for first-order ODEs for parallel computers. We investigate linear stability and derive methods with enlarged stability regions. In numerical experiments on a shared memory computer we compare a parallel variable step size EPTRK implementation with the efficient sequential Runge-Kutta method dopri5. Key words: Runge-Kutta methods, parallelism, two-step methods, stability AMS(MOS) subject classification (1991): 65M12, 65M20 1 Introduction For the numerical solution of systems of first-order ordinary differential equations (ODEs) y 0 = f(t; y); y(t 0 ) = y 0 ; y; f 2 R n ; (1) Fei [3], Cong [1] and Cong et al. [2] have recently investigated a class of explicit pseudo two-step Runge-Kutta methods (EPTRK methods). EPTRK methods compute an approximation um ß y(t m ) by the s-stage scheme Um+1 = 1l\Omega um + hm (Am\Omega I)F (t m\Gamma1 1l + hm\Gamma1 c; Um ); (2a) um+1 = um + hm (b T\Omega..