New high-accuracy non-polynomial spline group explicit iterative method for two-dimensional elliptic boundary value problems

In this paper, we propose a new high-accuracy method based on nonpolynomial spline for the numerical solution to two-dimensional elliptic partial differential equations. using a non-polynomial spline approximation in x-direction and central difference in y-direction, we obtain a new nine-point compact finite-difference formulation. a four-point group explicit (ge) iterative scheme with an acceleration tool is then applied to the obtained system. the formulation procedure is presented in detail. the efficiency of the proposed method is then illustrated by some test problems. the numerical results are found to be in good agreement with the exact solutions.