This paper deals with the non- Linear singular system from fluid dynamics. The results (approximate solutions) obtained using single-term Haar wavelet series and Leapfrog methods are compared with the exact solutions of the non-Linear singular system from fluid dynamics. It is found that the solution obtained using Leapfrog method is closer to the original solution of the non-Linear singular system from fluid dynamics. The high accuracy and the wide applicability of Leapfrog method approach will be demonstrated with numerical examples.