This work presents numerical methods for solving initial value problems in ordinary differential equations. Euler's method is presented from the point of view of Taylor's algorithm which considerably simplifies the rigorous analysis while Runge Kutta method attempts to obtain greater accuracy and at the same time avoid the need for higher derivatives by evaluating the given function at selected points on each subinterval. We discuss the stability and convergence of the two methods under consideration and result obtained is compared to the exact solution. The error incurred is undertaken to determine the accuracy and consistency of the two methods
