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ABSTRACT
In chapter one we introduced an overview of an ordinary differential equation and also a brief description of the numerical methods for the solution of ordinary differential equations and its uses in different fields of study. In chapter two we introduced the Euler’s method which was used to solve for a certain initial value problem and we got a numerical approximation which was close to the exact solution of the problem. In chapter three we introduced the Runge-Kutta method (2nd order) to solve some ODEs and arrived at an approximation for the solution, which we found to be more accurate than that of the Euler’s method. In chapter four we addressed the linear multistep method Adams Bashforth method which also gave us a numerical approximation for the initial value problem and discovered one of the drawbacks of the Adams Bashforth method was the necessity of using a previous method to begin its calculations.
