Two-Grid Approximations Applied to Solve Elliptic Equation

Two-Grid Approximations Applied to Solve Elliptic Equation

Elliptic Partial Differential Equations of second order have been studied using some numerical methods. This type of differential equations has specific applications in physical and engineering models. In most applications, first- order and second-order formulas are used for the derivatives. In this work higher order formulas such as: seven-points and nine-points formulas are used. Using these formulas will transform the partial differential equation into finite difference equations. To solve the resulting finite difference equations the following iterative methods have been used: Jacobi method, Gauss-Seidel method, Successive Over- Relaxation method (SOR) and Two-Grid method. Complete, working Matlab codes for each step are presented. The Matlab codes are straightforward and allow the reader to see the differences in implementation between different cases.