Biological growth curves are used to make predictions about natural growth phenomena and have an excellent record of success in several disciplines. A conventional approach is to treat the growth equations as mechanistic nonlinear models and fit them to real data sets by nonlinear least squares or maximum likelihood method. Bhowmick et al. (2014)'s method explicitly utilized the functional form of growth equations and obtained interval-specific estimates of parameters. These estimates have been found to perform better in estimating relative growth rate (RGR) and have the potential for selecting the best model from a set of competitive nonlinear models. Indeed the model-specific estimates of RGR have already been used in growth studies for model selection purposes. However, its computation involves a lengthy mathematical calculation, and many times explicit expressions for the interval-specific estimators are not available that are a function of data alone. For highly nonlinear models, where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. We propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. We found that the proposed strategy provides stable estimates compared to an existing approach involving several steps of mathematical calculations. It is also found to be robust when the process error has a significant variance. In addition, it does not require manual mathematical manipulation, instead, it uses available optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. The validity of the proposed estimation process has been carried out by both simulation studies and real data sets.