Many physical and scientific phenomena are modeled by nonlinear partial differential equations (NPDEs); it is difficult to handle nonlinear part of these equations. Recently some analytical methods are applied to solve such equations. In this work, modified Camassa-Holm and Degasperis-Procesi equation is studied. Adomian's decomposition method (ADM) is applied to obtain solution of this equation. The results are compared to those of homotopy perturbation method (HPM) and exact solution. The study highlights the significant features of the employed method and its ability to handle nonlinear partial differential equations.

Abstract-Construction ofalgorithmisa significant aspect in solving a problembefore being transferred totheprogramming language. Algorithm helped a user to do their job systematic and can be reduced working time. The real problem must be modeled into mathematical equation(s) before construct the algorithm. Then, the algorithm be transferred into programming code using computer software. In this paper, a numerical method as a platform problem solving tool and researcher used Scilab 5.4.0 Programming to solve the mathematical model such as Ordinary Differential Equations (ODE). There are various methodsthatcanbe usedin problem solvingODE. This research used to modify Euler's method because the method was simple and low computational. The main purposes of this research are to show the new algorithm for implementing the modify Euler's method and made comparisons between another modify Euler's and an exact value by integration solution. The comparison will be solved the ODE's using built-infunctions available in Scilab programming.