Rational methods with optimal order of convergence for partial differential equations
Tài liệu tham khảo
Abarbanel, 1996, On the removal of boundary errors caused by Runge–Kutta integration of nonlinear partial differential equations, SIAM J. Sci. Comput., 17, 777, 10.1137/S1064827595282520
Alonso-Mallo, 1999, Single step methods with optimal order of convergence for partial differential equations, Appl. Numer. Math., 31, 117, 10.1016/S0168-9274(98)00132-9
Alonso-Mallo, 1996, On the convolutions operators arising in the study of abstract initial boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A, 126, 515, 10.1017/S0308210500022897
Bendtsen, 1997, On implicit Runge–Kutta methods with high stage order, BIT, 37, 221, 10.1007/BF02510182
Brenner, 1979, On rational approximations of semigroups, SIAM J. Numer. Anal., 16, 683, 10.1137/0716051
Brenner, 1982, Single step methods for non-homogeneous linear differential equations in Banach spaces, RAIRO Anal. Numer., 16, 5, 10.1051/m2an/1982160100051
Carpenter, 1995, The theoretical accuracy of Runge–Kutta time discretizations for the initial boundary value problem: A study of the boundary error, SIAM J. Sci. Comput., 16, 1241, 10.1137/0916072
Hairer, 1991
Hersh, 1979, High-accuracy stable difference schemes for well-posed initial-value problems, SIAM J. Numer. Anal., 16, 670, 10.1137/0716050
Keeling, 1989, Galerkin/Runge–Kutta discretizations for parabolic equations with time-dependent coefficients, Math. Comp., 52, 561
Keeling, 1990, Galerkin/Runge–Kutta discretizations for semilinear parabolic equations, SIAM J. Numer. Anal., 27, 394, 10.1137/0727024
Koto, 1994, Explicit Runge–Kutta schemes for evolutionary problems in partial differential equations, Ann. Numer. Math., 1, 335
Lambert, 1991
Lee, 1994, Fully discrete methods for the nonlinear Schrödinger equation, Comput. Math. Appl., 28, 9, 10.1016/0898-1221(94)00148-0
Marchuk, 1983
Ortega, 1970
Ostermann, 1992, Runge–Kutta methods for partial differential equations and fractional orders of convergence, Math. Comp., 59, 403, 10.1090/S0025-5718-1992-1142285-6
Ostermann, 1993, Rosenbrock methods for partial differential equations and fractional orders of convergence, SIAM J. Numer. Anal., 30, 1084, 10.1137/0730056
Palencia, 1993, A stability result for sectorial operators in Banach spaces, SIAM J. Numer. Anal., 30, 1373, 10.1137/0730071
Palencia, 1994, On the stability of variable step-size rational methods for holomorphic semigroups, Math. Comp., 62, 93, 10.1090/S0025-5718-1994-1201070-9
Palencia, 1994, Abstract initial boundary values problems, Proc. Roy. Soc. Edinburgh Sect. A, 124, 879, 10.1017/S0308210500022393
Pathria, 1997, The correct formulation of intermediate boundary conditions for Runge–Kutta time integration of initial boundary value problems, SIAM J. Sci. Comput., 18, 1255, 10.1137/S1064827594273948
Pazy, 1983
Sanz-Serna, 1984
Sanz-Serna, 1989, Stability and convergence at the PDE/stiff ODE interface, Appl. Numer. Math., 5, 117, 10.1016/0168-9274(89)90028-7
Sanz-Serna, 1986, Convergence and order reduction of Runge Kutta schemes applied to evolutionary problems in partial differential equations, Numer. Math., 50, 405, 10.1007/BF01396661
Spijker, 1995, Error growth analysis via stability regions for discretizations of initial value problems, BIT, 32, 442
Verwer, 1986, Convergence and order reduction of diagonally implicit Runge–Kutta schemes in the method of lines, 140, 220