Two one-parameter families of fourth order finite difference discretizations of the Dirichlet problem for the Helmholtz equation a 2 u/ax 2 + ij2 uJa y2 + Fu = G on a rectangle are presented. The general suitabil~ty of several standard iterative techniques for the solution .to the resulting systems of linear equations are discussed. Some numerical results are presented which indicate that such ...

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-E...

We present two tools, which could be useful in determining whether or not a non-Homogenous Linear Recurrence can reach a desired rational. First, we derive the determinant that is equal to the i term in a non-Homogenous Linear Recurrence. We use this to derive the infinite determinant that is zero, if and only if, the desired rational can be reached by some term in the recurrence. Second, we de...