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The mixture of Laplace transform and Homotopy perturbation was used to solve Benjamin-Bona-Mahony problems. In this research work, three examples of Benjamin-Bona-Mahony equations were considered. The numerical solutions were obtained by Laplace Homotopy Perturbation method. The method was introduced as essential tool to linearize all the associated nonlinear terms in the equations since Laplace transform method alone cannot handle nonlinear terms. The solutions are series form which quickly converges precisely to their exact value with few iterations. The solution obtained by Laplace Homotopy perturbation method accord well with solutions obtained by using other existing methods. The method of Laplace Homotopy perturbation is very powerful integral transform methods in solving some nonlinear Equations like Benjamin-Bona-Mahony equations. [ABSTRACT FROM AUTHOR]

In this paper, two methods Adomian Decomposition Method (ADM) and Laplace Adomian Decomposition Method (LADM) were adopted to solve the telegraph equation. The essence of this research is to establish a relationship between the two analytical methods. It was observed that the two methods were consistent as the results obtained from the numerical examples on the two methods were the same. We also generated the telegraph equation to help provide a solid basis for the application of the telegraph equation. The telegraph equation is one of the nonlinear partial differential equation and it’s application to solving practical problems were suggested for further studies. [ABSTRACT FROM AUTHOR]