Three-step BLAGE iterative method for two-dimensional elliptic boundary value problems with singularity

Abstract

We present a new three-step block alternating group explicit (BLAGE) algorithm for solving block symmetric linear systems derived from both five-point second-order and nine-point fourth-order discretizations to solve the two-dimensional elliptic equation in both rectangular and cylindrical polar coordinates. The three-step BLAGE algorithm should save time compared with the two-step BLAGE algorithm as the aim of the procedure is to eliminate the evaluation of two similar terms which appear in the algorithm. The convergence theory of the algorithm is reported briefly. Numerical results obtained from three test problems are presented to demonstrate the utility of the proposed three-step BLAGE method compared with the corresponding two-step BLAGE iterative method and the block successive over-relaxation (BSOR) iterative method.

^† Dedicated to the late Professor D.J. Evans

Keywords:

• Fourth-order compact scheme
• Diffusion–convection equation
• Cylindrical polar coordinates
• Three-step BLAGE method
• Poisson equation
• Tri-diagonal solver

Notes

^† Dedicated to the late Professor D.J. Evans