Abstract:
The purpose of this project is to propose a great deal of interest to improve the Euler
methods of solving initial value problems in ordinary differential equations because of its
easy implementation and low computational cost. In this report the absolute stability and
convergence of third order Euler method is discussed. Furthermore, algorithms to some
numerical experiments have been given to demonstrate the conclusions. The computation
al results show that the method is consistent accurate and convergent of order 3. Succinct
overviews of its basic properties necessary for the selection of a good numerical method
in the development of program codes are also presented. Finally, the results are presented
by using graphs.
