This project is on the numerical solution of partial differential equations. In this project a mathematical model is formulated together with its boundary conditions. Finite elements and finite difference methods are used to solve the problem. This project is intended for students taking mathematics courses especially Numerical solution of partial differential equations as a base on how to solve initial value problems numerically. This also will help students to explore some basics on matlab coding. It is my believe that any one who reads this project will benefit more.