In this article, the practical and important problems have been considered, the inhomogeneous problems by an application of the Leapfrog method. The numerical solutions are presented with an example, with an initial condition (discussed by Sekar et al. [1]) having two different solutions, to illustrate and demonstrate the efficiency of the proposed method. The solution graphs are presented to highlight the efficiency of the Leapfrog method. © 2021 Elsevier B.V., All rights reserved.