Adomian decomposition method for a reliable treatment of the Bratu-type equations

In this paper, we present a framework to determine exact solutions of Bratu-type equations. The algorithm rests mainly on the Adomian decomposition method. The proposed scheme is illustrated by studying two boundary value problems and an initial value problem of Bratu-type. The first type gives a solution that blows up at the middle of the domain, whereas the other equations give bounded solutions.