The purpose of the current investigations is to solve the nonlinear dynamics based on the nervous stomach model (NSM) using the supervised neural networks (SNNs) along with the novel features of Levenberg- Marquardt backpropagation technique (LMBT), i.e., SNNs-LMBT. The SNNs-LMBT is implemented with three different types of sample data, authentication, testing and training. The ratios for these statistics to solve three different variants of the nonlinear dynamics of the NSM are designated 75% for training, 15% for validation and 10% for testing, respectively. For the numerical measures of the nonlinear dynamics of the NSM, the Runge- Kutta scheme is implemented to form the reference dataset. The attained numerical form of the nonlinear dynamics of the NSM through the SNNs- LMBT is implemented in the reduction of the mean square error (MSE). For the exactness, competence, reliability and efficiency of the proposed SNNs-LMBT, the numerical actions are capable using the proportional arrangements through the features of the MSE results, error histograms (EHs), regression and correlation.