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Jumat Sulaiman
Universiti Malaysia Sabah

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Solutions of reaction-diffusion equations using similarity reduction and HSSOR iteration Nur Afza Mat Ali; Rostang Rahman; Jumat Sulaiman; Khadizah Ghazali
Indonesian Journal of Electrical Engineering and Computer Science Vol 16, No 3: December 2019
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v16.i3.pp1430-1438

Abstract

Similarity method is used in finding the solutions of partial differential equation (PDE) in reduction to the corresponding ordinary differential equation (ODE) which are not easily integrable in terms of elementary or tabulated functions. Then, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is applied in solving the sparse linear system which is generated from the discretization process of the corresponding second order ODEs with Dirichlet boundary conditions. Basically, this ODEs has been constructed from one-dimensional reaction-diffusion equations by using wave variable transformation. Having a large-scale and sparse linear system, we conduct the performances analysis of three iterative methods such as Full-sweep Gauss-Seidel (FSGS), Full-sweep Successive Over-Relaxation (FSSOR) and HSSOR iterative methods to examine the effectiveness of their computational cost. Therefore, four examples of these problems were tested to observe the performance of the proposed iterative methods.  Throughout implementation of numerical experiments, three parameters have been considered which are number of iterations, execution time and maximum absolute error. According to the numerical results, the HSSOR method is the most efficient iterative method in solving the proposed problem with the least number of iterations and execution time followed by FSSOR and FSGS iterative methods.
Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation Nur Farah Azira Zainal; Jumat Sulaiman; Azali Saudi; Nur Afza Mat Ali
Indonesian Journal of Electrical Engineering and Computer Science Vol 29, No 3: March 2023
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v29.i3.pp1606-1613

Abstract

This paper proposes the combination of a preconditioner applied with successive over relaxation (SOR) iterative method for solving a sparse and huge scale linear system (LS) in which its coefficient matrix is a tridiagonal matrix. The purpose for applying the preconditioner is to enhance the convergence rate of SOR iterative method. Hence, in order to examine the feasibility of the proposed iterative method which is preconditioner SOR (PSOR) iterative method, first we need to derive the approximation equation of one-dimensional (1D) Burgers’ equation through the discretization process in which the second-order implicit finite difference (SIFD) scheme together with semi-approximate (SA) approach have been applied to the proposed problem. Then, the generated LS is modified into preconditioned linear system (PLS) to construct the formulation of PSOR iterative method. Furthemore, to analyze the feasibility of PSOR iterative method compared with other point iterative methods, three examples of 1D Burgers’ equation are considered. In conclusion, the PSOR iterative method is superior than PGS iterative method. The simulation results showed that our proposed iterative method has low iteration numbers and execution time.
Co-Authors Azali Saudi Khadizah Ghazali Nur Afza Mat Ali Nur Farah Azira Zainal Rostang Rahman