Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

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

Ascher, 1995, Implicit-explicit methods for time-dependent PDE's, SIAM J. Numer. Anal., 32, 797, 10.1137/0732037

Canuto, 1987

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

Crouziex, 1980, Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques, Numer. Math., 35, 257, 10.1007/BF01396412

Griepentrog, 1978, Gemischte Runge-Kutta-verfahren für steife systeme, 11, 19

Hairer, 1993

Hairer, 1991

Karniadakis, 1991, High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 97, 414, 10.1016/0021-9991(91)90007-8

Kim, 1985, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59, 308, 10.1016/0021-9991(85)90148-2

Ruuth, 1995, Implicit-explicit methods for reaction-diffusion problems in pattern formation, J. Math. Biol., 34, 148, 10.1007/BF00178771

Skeel, 1997, A family of symplectic integrators: stability, accuracy, and molecular dynamics applications, SIAM J. Sci. Comput., 18, 203, 10.1137/S1064827595282350

Spiteri, 1995, Numerical solution of differential systems with algebraic inequalities arising in robot programming

Turek, 1996, A comparative study of time stepping techniques for the incompressible Navier-Stokes equations: from fully implicit non-linear schemes to semi-explicit projection methods, Internat. J. Numer. Methods Fluids, 22, 987, 10.1002/(SICI)1097-0363(19960530)22:10<987::AID-FLD394>3.0.CO;2-7

Varah, 1980, Stability restrictions on second order, three level finite difference schemes for parabolic equations, SIAM J. Numer. Anal., 17, 300, 10.1137/0717025

Verwer, 1996, An implicit-explicit approach for atmospheric transport-chemistry problems, Appl. Numer. Math., 20, 191, 10.1016/0168-9274(95)00126-3