Numerical solutions via maple and numerical methods of some particular boundary value problems and initial value problems

In this thesis, It has been studied on the numerical solutions of some particular types of second order nonlinear boundary and initial value problems. For boundary value problems, shooting method has been used to transform the second order nonlinear ordinary differential equation into two initial value problems and numerical solutions have been obtained by the fourth order Runge-Kutta method with using the package programme Maple 11. For some cases, the approximate solutions results have been compared with analytical solutions. As an initial value problem, Van der Pol equation or ordinary differential called Van der Pol ossilator, which is a second order nonlinear equation and models the ossilacions in an electronic circuit, have been considered. For different paramaters and initial conditions, approximate solutions have been obtained again by the fourth order Runge-Kutta method and via Maple 11. The results have been illustrated by the help of tables and graphics.