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

In this paper, ongoing studies to investigate nonlinear ordinary dierentialequations (ode) are extended by presenting a new concept in non-dimensionalizationprocess. this concept is illustrated with a practical example of nonlinear odes, whichcannot reliably solve using the numerical methods. in this paper, two perturbationtechniques are used to solve the problem. eect of varying the dimensionless initialdisplacement on the accuracy of solution is investigated. it is shown that if the processof non-dimensionalizing is done appropriately, the calculated results will be extremelyaccurate. moreover, a new concept called behavior of results is proposed to nd accurateresults.