An ecient concept for non-dimensionalizing the dung equations based on the parameterized perturbation method

In this paper, ongoing studies to investigate nonlinear Ordinary Dierential Equations (ODE) are extended by presenting a new concept in non-dimensionalization process. This concept is illustrated with a practical example of nonlinear ODEs, which cannot reliably solve using the numerical methods. In this paper, two perturbation techniques are used to solve the problem. Eect of varying the dimensionless initial displacement on the accuracy of solution is investigated. It is shown that if the process of non-dimensionalizing is done appropriately, the calculated results will be extremely accurate. Moreover, a new concept called \behavior of results" is proposed to nd accurate results.