Estimation of the Number of Iterations for Detinite Convergence Condition by Use of the Gauss-Seidel Method

In this investigation the estimation method of the number of iterations for definite convergence condition by use of the Gauss-Seidel method applied for a set of linear equations which is obtained from the finite element analysis (or the finite difference analysis) of any rectangular area subdivided into N*M is proposed. Though thenumber of iterations can be obtained by using the eigenvalue of the governing equations, the proposed method does not require the eigenvalue but only the values of Nand M. Numerical experiments on this estimation method clarifythat the estimated values are within the error bound of 10%.