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Abstract. In this paper, a new fourth-order nine-point finite difference scheme based on the rotated grid combined with the traditional Successive Over Relaxation (SOR)-type iterative method is discussed in solving the two-dimensional convection-diffusion partial differential equation (pde) with variable coefficients. Numerical experiments are carried out to verify the high accuracy solution of the scheme. Comparisons with the exact solutions also show that the rotated scheme converges faster than the existing compact scheme of the same order.

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Abstract. The formulation and implementation of a new explicit group method in solving the two dimensional (2D) elliptic partial differential equation (PDE) is presented. The fourth order group scheme is derived from the rotated ninepoint finite difference discretization formula applied to the Poisson equation. Numerical solutions are obtained for different mesh sizes. The iterative procedure of the Fourth Order Modified Explicit Decoupled Group (FOMEDG) method is found to require lesser execution timings and iteration numbers compared to the existing Fourth Order Modified Explicit Group (FOMEG) method resulting in faster convergence rate.