Konvergenz von Mehrschrittverfahren zur Lösung halblinearer Anfangswertaufgaben

Lax andRichtmyer showed, that stability of multi-level difference approximations to linear ordinary or partial initial value problems is sufficient as well as necessary for convergence.Dahlquist showed, that his stability concept for multi-level difference approximations to a system of non-linear first order ordinary differential equations yields a necessary and sufficient condition for convergence too. Here, the Lax-Richtmyer-theory is extended to semi-linear initial value problems, including now both convergence theorems.