Final Year Project : Numerical Method for Solving Elliptic Equation by Using Difference Discretization Scheme and Comparing Basic Iterative Solution with Graphical User Interface (GUI) Group members : Nur Iman Nazirah , Nur Izni Syahirah, Siti Aisyah Final Year Project Supervisor : Associate Professor Dr Nor Azni Binti Shahari
Partial Differential Equation (PDE) can be used as a topic in solving the science and engineering applications. PDE consists of Elliptic Equation, Wave Equation and Heat Equation. In this research we aimed to focus on solving an Elliptic Equation by using Numerical Method. Finding the analytical solution for Elliptic Equation can be tedious. Thus in this research we solve an Elliptic Equation numerically. Numerical method for boundary value problem can be solved by using Graphical User Interface in MATLAB. The main purpose for this project is to discretize the Elliptic Equation by using difference discretization technique and solve the Elliptic Equation by using difference method of linear system. The method we have use are Finite Difference Method(FDM) and Crank Nicolson for discretization, then to solve the linear system we use Jacobi, Gauss-Seidel, Successive Over Relaxation, Conjugate Gradient method and Preconditioned Conjugate Gradient method. Lastly, the results are obtained which leads to Finite Differences are more accurate than Crank Nicolson. Therefore, several investigations need to carry out to determine the application of Elliptic Equation.