Accelerated Overrelaxation Method for the Solution of Discrete Laplace’s equation on a Rectangle

On a rectangle given the Dirichlet Laplace’s equation, for its solution by finite differences there exist numerous direct methods and iterative methods. Examples of direct methods are block decomposition, block elimination, block cyclic reduction methods, discrete Fourier transform methods. Among the iterative methods, Successive Overrelaxation Methods, Accelerated Overrelaxation Method (AOM), are widely used methods. In this thesis we studied the Accelerated Overrelaxation Method (AOR) for the numerical solution of discrete Laplace’s equation on a rectangle obtained by 5-point difference scheme. Numerical results are given for different values of the two parameters, w and r and for mesh size . h