On the performance of three iterative methods for solution of GDQ algebraic equations Original Research Article

In this paper, the three conventional iterative methods, namely, J-OE (or Jacobi), Gauss-Seidel (G-S), and SOR methods are extended to solve the GDQ algebraic equations. The performances of these three iterative methods for the GDQ and second-order finite difference (FD) algebraic equations are comparatively studied by their application to solve the two-dimensional Poisson equation. It was found that SOR method gives the fastest convergence rate for both GDQ and FD algebraic equations. However, the effect of relaxation factor for GDQ algebraic equations is reduced. The high efficiency and accuracy of GDQ over second order FD scheme are also shown in the paper. Furthermore, the performance of J-OE and SOR methods was validated by their application to a complicated problem, that is, numerical simulation of natural convection in the annulus between two concentric cylinders. It was found that for this complicated case, Jacobi and Gauss-Seidel methods cannot get converged solution, and the efficiency of SOR method is reduced to be around three times faster than the J-OE method.