P-stability properties of runge-kutta methods for delay differential equations
Numerische Mathematik
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
On the stability of implicit-explicit linear multistep methods
Applied Numerical Mathematics - Special issue on time integration
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
IMEX Runge-Kutta schemes for reaction-diffusion equations
Journal of Computational and Applied Mathematics
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Stability of IMEX (implicit-explicit) Runge-Kutta methods applied to delay differential equations (DDEs) is studied on the basis of the scalar test equation du/dt=@lu(t)+@mu(t-@t), where @t is a constant delay and @l,@m are complex parameters. More specifically, P-stability regions of the methods are defined and analyzed in the same way as in the case of the standard Runge-Kutta methods. A new IMEX method which possesses a superior stability property for DDEs is proposed. Some numerical examples which confirm the results of our analysis are presented.