Construction of highly stable two-step W-methods for ordinary differential equations

Bartoszewski, 1998, Construction of two-step Runge–Kutta methods of high order for ordinary differential equations, Numer. Algorithms, 18, 51, 10.1023/A:1019157029031 Butcher, 2001, General linear methods for stiff differential equations, BIT, 41, 240, 10.1023/A:1021986222073 Butcher, 1996, Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations, Appl. Numer. Math., 21, 385, 10.1016/S0168-9274(96)00043-8 Butcher, 1998, Construction of high order diagonally implicit multistage integration methods for ordinary differential equations, Appl. Numer. Math., 27, 1, 10.1016/S0168-9274(97)00109-8 Butcher, 1997, A nonlinear optimization approach to the construction of general linear methods of high order, J. Comput. Appl. Math., 81, 181, 10.1016/S0377-0427(97)00039-3 Guglielmi, 2001, On the asymptotic properties of a family of matrices, Linear Algebra Appl., 322, 169, 10.1016/S0024-3795(00)00228-7 Guglielmi, 2001, On the zero-stability of variable step-size multistep methods, Numer. Math., 88, 445, 10.1007/s211-001-8010-0 Hairer, 1996 Hochbruck, 1998, Exponential integrators for large systems of differential equations, SIAM J. Sci. Comput., 19, 1552, 10.1137/S1064827595295337 Z. Jackiewicz, Error estimation and control for two-step W-methods, in preparation. Jackiewicz, 1999, Exploiting structure in the construction of DIMSIMs, J. Comput. Appl. Math., 107, 233, 10.1016/S0377-0427(99)00091-6 Jackiewicz, 1995, A general class of two-step Runge–Kutta methods for ordinary differential equations, SIAM J. Numer. Anal., 32, 1390, 10.1137/0732064 Kaps, 1979, Generalized Runge–Kutta methods of order four with stepsize control for stiff ordinary differential equations, Numer. Math., 38, 55, 10.1007/BF01396495 Kreiss, 1978, Difference methods for stiff ordinary differential equations, SIAM J. Numer. Anal., 15, 21, 10.1137/0715003 Lambert, 1973 H. Podhaisky, Parallele Zweischritt-W-Methoden, Ph.D. Thesis, Martin-Luther-Universität, Halle-Wittenberg, 2002. H. Podhaisky, B.A. Schmitt, R. Weiner, Two-step W-methods with parallel stages, Report 22, Institute of Numerical Mathematics, Martin-Luther-Universität, Halle-Wittenberg, 1999. Podhaisky, 2002, Design, analysis and testing of some parallel two-step W-methods for stiff systems, Appl. Numer. Math., 42, 381, 10.1016/S0168-9274(01)00162-3 Schmitt, 1998, Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs, BIT, 38, 391, 10.1007/BF02512374 Weiner, 2002, Two-step W-methods on singular perturbation problems, Vol. 2328, 778