Indonesian Journal of Electrical Engineering and Computer Science Vol. 23, No. 1, July 2021, pp. 471~478 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v23.i1.pp471-478  471 Journal homepage: http://ijeecs.iaescore.com Performance of similarity explicit group iteration for solving 2D unsteady convection-diffusion equation Nur Afza Mat Ali 1 , Jumat Sulaiman 2 , Azali Saudi 3 , Nor Syahida Mohamad 4 1,2,4 Faculty of Science and Natural Resources, Universiti Malaysia Sabah (UMS), Malaysia 3 Faculty of Computing and Informatics, Universiti Malaysia Sabah (UMS), Malaysia Article Info ABSTRACT Article history: Received Mar 31, 2021 Revised Jun 8, 2021 Accepted Jun 17, 2021 In this paper, a similarity finite difference (SFD) solution is addressed for the two-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization scheme to get the second-order SFD approximation equation. We propose a four- point similarity explicit group (4-point SEG) iterative method as a numerical solution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To show the 4-point SEG iteration efficiency, two iterative methods, such as Jacobi and Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's performance. Finally, the numerical results showed that our proposed iterative method is more efficient than the Jacobi and GS iterations in terms of iteration number and execution time. Keywords: Convection-diffusion equation Partial differential equation Similarity explicit group Similarity finite difference Similarity solution This is an open access article under the CC BY-SA license. Corresponding Author: Jumat Sulaiman Faculty of Science and Natural Resources Universiti Malaysia Sabah Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia Email: jumat@ums.edu.my 1. INTRODUCTION Convection-diffusion equation (CDE) is one of the most challenging problems and frequently used in various branches of engineering and applied science, especially in radial transport in a porous medium [1], heat transfer in a nanofluid filled [2], heat transfer in a draining film [3], and water transport in soil [4]. Also, the applications of CDE can be found in [5]-[8]. Due to its application, these problems have received extensive attention, and many researchers attempted to solve these problems numerically to achieve the lowest computational complexity and highest performance. To achieve the low computational complexity, there are many studies on similarity solution techniques have been explored by many researchers and applied in partial differential equations (PDEs). For instance, Afify [9] presented similarity solutions in magnetohydrodynamic, which is obtained by using scaling transformations then solved numerically by using the shooting technique with fourth-order Runge–Kutta integration scheme. M. Siavashi et al. [10], the authors obtained a similarity solution of air and nanofluid impingement cooling of a cylindrical porous heat sink using similarity variables then solved numerically. Usman et al. [11], a similarity solution of the water/magnetite nanofluid modelled PDEs subject to thermal radiation and Lorentz force over stretchable rotating disks is obtained by supporting precise similarity transformation. The studies on the similarity