Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.

The present paper proposes a mathematical method to numerically treat class of third-order linear Boundary Value Problems (BVPs). This is based on the combination Adomian Decomposition Method (ADM) and, modified shooting method. A complete derivation proposed has been provided, in addition its numerical implementation validation via utilization Runge-Kutta other existing methods. applied divers...