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Adomian decomposition method for a reliable treatment of the Bratu-type equations. (English) Zbl 1073.65068

Summary: 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.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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