On the Internal Stability of Explicit, m‐Stage Runge‐Kutta Methods for Large m‐Values

Explicit, m‐stage Runge‐Kutta methods are derived for which the maximal stable integration step per right hand side evaluation is proportional to m when applied to semi‐discrete parabolic initial‐boundary value problems. The internal stability behaviour of these methods is compared with that of similar Runge‐Kutta methods proposed in the literature. Both by analysis and by numerical experiments we show that the value of m in the schemes proposed in this paper is not restricted by internal instabilities.