Characterizing strong stability preserving additive Runge-Kutta methods. (English) Zbl 1203.65109
Summary: Space discretization of some time dependent partial differential equations give rise to ordinary differential equations containing additive terms with different stiffness properties. In these situations, additive Runge-Kutta (additive RK) methods are used. For additive RK methods the curve of absolute monotonicity gives stepsize restrictions for monotonicity. Necessary conditions for nontrivial curves of absolute monotonicity are the nonnegativity of the additive RK coefficients and some inequalities on some incidence matrices. In this paper we characterize strong stability preserving additive Runge-Kutta methods giving some order barriers and structural properties.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
Keywords:
Runge-Kutta; additive Runge-Kutta; strong stability preserving; SSP; absolutely monotonic; radius of absolute monotonicity; nonnegative coefficientsReferences:
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