Finding approximate solutions for a class of third-order non-linear boundary value problems via the decomposition method of Adomian

Abstract

Third-order boundary value problems (BVPs) were discussed in many papers in recent years. The existence of solutions to these problems is shown under certain conditions. Finding the exact or approximate solution of these problems is not easy especially when the boundary conditions are non-linear. In this paper, we present a method for solving a class of third-order BVPs with non-linear boundary conditions. The decomposition procedure of Adomian is used for solving these problems and the advantages of this method over the other existing methods are shown. Numerical results are presented to show the efficiency of the developed method.

Keywords:

• third-order non-linear boundary value problems
• Adomian decomposition method
• closed form solution

2000 AMS Subject Classification: :

• 34A25
• 34B99
• 34L30
• 65L10
• 65L99

Acknowledgement

The authors are very grateful to the three reviewers and the subject editor for carefully reading the paper and for their comments and suggestions which have greatly improved the paper.