Generalized ROW-type methods for solving semi-explicit DAEs of index-1
Tài liệu tham khảo
Steihaug, 1979, An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations, Math. Comp., 33, 521, 10.1090/S0025-5718-1979-0521273-8
Rentrop, 1985, Partitioned Runge–Kutta methods with stiffness detection and stepsize control, Numer. Math., 47, 545, 10.1007/BF01389456
Hundsdorfer, 2003, vol. 33
Weiner, 1992, Linear-implizite Runge–Kutta Methoden und ihre Anwendung, vol. 127
Kaps, 1989, Rosenbrock methods using few LU-decompositions, IMA J. Numer. Anal., 9, 15, 10.1093/imanum/9.1.15
Roche, 1988, Rosenbrock methods for differential algebraic equations, Numer. Math., 52, 45, 10.1007/BF01401021
Rentrop, 1989, The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations, Numer. Math., 55, 545, 10.1007/BF01398915
Strehmel, 1990, On error behaviour of partitioned linearly implicit Runge–Kutta methods for stiff and differential algebraic systems, BIT, 30, 358, 10.1007/BF02017354
T. Jax, G. Steinebach, ROW Methods Adapted to Network Simulation for Fluid Flow, (in press) in: Progress in Industrial Mathematics at ECMI 2014, G. Russo, V. Capasso, G. Nicosia, V. Romano (Eds.), The European Consortium for Mathematics in Industry, vol. 22, Springer-Verlag, 2016.
Hairer, 2002, vol. 14
Hairer, 2008, vol. 8
Rang, 2005, New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index 1, BIT, 45, 761, 10.1007/s10543-005-0035-y
Deuflhard, 1987, One-step and extrapolation methods for differential-algebraic systems, Numer. Math., 51, 501, 10.1007/BF01400352
Scholz, 1989, Order barriers for the B-convergence of ROW methods, Computing, 41, 219, 10.1007/BF02259094
Ostermann, 1993, Rosenbrock methods for partial differential equations and fractional orders of convergence, SIAM J. Numer. Anal., 30, 1084, 10.1137/0730056
Rang, 2014, An analysis of the Prothero–Robinson example for constructing new DIRK and ROW methods, J. Comput. Appl. Math., 262, 105, 10.1016/j.cam.2013.09.062
G. Steinebach, Order-reduction of ROW-methods for DAEs and Method of Lines Applications, Preprint 1741, Technische Universität Darmstadt, Darmstadt, 1995.