Sharif University of Technology Scientia Iranica 1026-3098 24 6 2017 12 01 New High Accuracy Non-polynomial Spline Group Explicit Iterative Method for Two Dimensional Elliptic Boundary Value Problems 3181 3192 4487 10.24200/sci.2017.4487 EN Joan Goh School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia Norhashidah Hj. M. Ali School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia Journal Article 2015 09 09 In this paper, we propose a new high accuracy method based on non-polynomial spline for the numerical solution of two-dimensional elliptic partial dierential equations. Using a non-polynomial spline approximation in the xdirection and central dierence in the y- direction, we obtain a new nine-point compact finite dierence 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 eciency 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 https://scientiairanica.sharif.edu/article_4487_932d0d053f6f8b53db2468608694e903.pdf