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Articles by J. Sulaiman
Total Records ( 12 ) for J. Sulaiman
  W. S. Koh , J. Sulaiman and R. Mail
  Problem statement: Modified Gauss-Seidel (MGS) was developed in order to improve the convergence rate of classical iterative method in solving linear system. In solving linear system iteratively, it takes longer time when many computational points involved. It is known that by applying quarter-sweep iteration scheme, it can decrease the computational operations without altering the accuracy. In this study, we investigated the effectiveness of the new Quarter-Sweep Projected Modified Gauss-Seidel (QSPMGS) iterative method in solving a Linear Complementarity Problem (LCP). Approach: The LCP we looked into is the LCP arise in American option pricing problem. Actually, American option is a Partial Differential Complementarity Problem (PDCP). By using full-, half- and quarter-sweep Crank-Nicolson finite difference schemes, the problem was reduced to Linear Complementarity Problem (LCP). Results: Several numerical experiments were carried out to test the effectiveness of QSPMGS method in terms of number of iterations, computational time and Root Mean Square Error (RMSE). Comparisons were made with full-, half- and quarter-sweep algorithm based on Projected Gauss-Seidel (PGS) and Projected Modified Gauss-Seidel (PMGS) methods. Thus, the experimental results showed that the QSPMGS iterative method has the least number of iterations and shortest computational time. The RMSE of all tested methods are in good agreement. Conclusion: QSPMGS is the most effective among the tested iterative methods in solving LCP whereby it is fastest and the accuracy remains the same.
  M. K. Hasan , J. Sulaiman , S. Ahmad , M. Othman and S. A.A. Karim
  Problem statement: Development of mathematical models based on set of observed data plays a crucial role to describe and predict any phenomena in science, engineering and economics. Therefore, the main purpose of this study was to compare the efficiency of Arithmetic Mean (AM), Geometric Mean (GM) and Explicit Group (EG) iterative methods to solve system of linear equations via estimation of unknown parameters in linear models. Approach: The system of linear equations for linear models generated by using least square method based on (m+1) set of observed data for number of Gauss-Seidel iteration from various grid sizes. Actually there were two types of linear models considered such as piece-wise linear polynomial and piece-wise Redlich-Kister polynomial. All unknown parameters of these models estimated and calculated by using three proposed iterative methods. Results: Thorough several implementations of numerical experiments, the accuracy for formulations of two proposed models had shown that the use of the third-order Redlich-Kister polynomial has high accuracy compared to linear polynomial case. Conclusion: The efficiency of AM and GM iterative methods based on the Redlich-Kister polynomial is superior as compared to EG iterative method.
  M.K. Hasan , J. Sulaiman , S.A.A. Karim and M. Othman
  The objective of this study was to describe numerical methods that apply complexity reduction approach to solve various scientific problems. Due to their low in complexity, their computations are faster than their standard form. Some of the methods have even higher in accuracy compared to their standard methods. In this study, we will describe the development of some of the methods that have been recently used to solve various scientific problems.
  S.A.A. Karim , B.A. Karim , M.T. Ismail , M.K. Hasan and J. Sulaiman
  The development of wavelet theory in recent years has motivated the emergence of applications such as in signal processing, image and function representation, finance, economics, numerical method etc. One of the dvantages wavelet as compared with Fourier is, it has fast algorithm to evaluate the series expansion. In the present study, we will discuss the applications of fast wavelet algorithm namely Discrete Wavelet Transform (DWT) in finance such as denoising the time series by using wavelet thresholding. Some numerical results by using real data will be presented.
  N.I.M. Fauzi and J. Sulaiman
  The aim of this study is to describe the formulation of Quarter-Sweep Modified Successive Over-Relaxation (QSMSOR) iterative method using cubic polynomial spline scheme for solving second order two-point linear boundary value problems. To solve the problems, a linear system will be constructed via discretization process by using cubic spline approximation equation. Then the generated linear system has been solved using the proposed QSMSOR iterative method to show the superiority over Full-Sweep Modified Successive Over-Relaxation (FSMSOR) and Half-Sweep Modified Successive Over-Relaxation (HSMSOR) methods. Computational results are provided to illustrate the effectiveness of the proposed method.
  A.A. Dahalan , N.S.A. Aziz and J. Sulaiman
  This study deals with the application of numerical methods in solving the Fuzzy Boundary Value Problems (FBVPs) which is discretized to derive second order fuzzy finite difference approximation equation. Then this fuzzy approximation equation is used to generate the fuzzy linear system. In addition to that, the fuzzy linear system will be solved iteratively by using Gauss-Seidel (GS), Full-Sweep Successive Over-Relaxation (FSSOR), Half-Sweep Successive Over Relaxation (HSSOR) and Quarter-Sweep Successive Over Relaxation (QSSOR) iterative methods. Then several numerical experiments are conducted to illustrate the effectiveness of QSSOR iterative method compared with the GS, FSSOR and QSSOR methods.
  A.A. Dahalan , N.A. Shattar and J. Sulaiman
  In this study, the iterative methods particularly families of Alternating Group Explicit (AGE) methods are used to solve finite difference algebraic equation arising from fuzzy diffusion equation is examined. For the proposed problems, family of AGE methods namely Full-Sweep AGE (FSAGE) and Half-Sweep AGE (HSAGE) has been considered to be the generated linear solver. The formulation and implementation of these two proposed methods were also presented. In addition, numerical results by solving two test problems are included and compared with the Full-Sweep Gauss Seidel (FSGS), FSAGE and HSAGE methods to show their performance.
  A.A. Dahalan , N.S.A. Aziz and J. Sulaiman
  In this study, system of linear equation is solved by using iterative method which is family of Alternating Group Explicit (AGE) generated from discretization of two point Fuzzy Boundary Value Problem (FBVPs). In addition, to that the fuzzy linear system has been solved iteratively by using Gauss-Seidel (GS), Full-Sweep AGE (FSAGE), Hall-Sweep AGE (HSAGE) and Quarter-Sweep AGE (QSAGE). Then numerical experiments are carried out onto two examples to verify the effectiveness of the method. Results show that the QSAGE method is superior than the other three methods in terms of execution time, number of iterations and Hausdorff distance.
  A.A. Dahalan , J. Sulaiman and N.S.A. Aziz
  In this study, iterative methods particularly the Alternating Group Explicit (AGE) iterative method is used to solve system of linear equations generated from the discretization of Two-Dimensional Fuzzy Poisson problems (2DFP). The formulation and implementation of the AGE method is also presented. Then numerical experiments are carried out on to two problems to verify the effectiveness of the methods. The results show that the AGE method is superior compared to GS method in terms of number of iterations, execution time and Hausdorff distance.
  J.V.L. Chew and J. Sulaiman
  This study considers the implicit finite difference solution of 1-Dimensional Porous Medium Equations (1D PMEs) using Half-Sweep Newton-Explicit Group (HSNEG) iterative method. The general finite difference approximation equation of 1D PME is formulated using the half-sweep implicit finite difference scheme. The generated nonlinear system is then solved using the proposed HSNEG iterative method. The comparative analysis is shown using two tested iterative methods namely Newton-Gauss-Seidel (NGS) and Newton-Explicit Group (NEG). The numerical results support the finding that the HSNEG is more superior than the NGS and the NEG in terms of total iterations and computation time. All three executed iterative methods showed good accuracy in solving 1D PME.
  A.A. Dahalan , A. Saudi and J. Sulaiman
  In recent years, a significant amount of research on robot path planning problems has been devoted. The main goal of this problem is to construct a collision-free path from arbitrary start location to a specified end position in their environment. In this study, numerical technique, specifically on family of Accelerated Over-Relaxation (AOR) iterative methods will be used in attempt to solve mobile robot problem iteratively. It’s lean on the use of Laplace’s equation to constrain the generation of a potential values. By applying a finite-difference technique, the experiment shows that it is able to generate smooth path between the starting positions to specified destination. The simulation results shows the proposed methods performs faster solution and smoother path compared to the previous research.
  J.J. Kiram , J. Sulaiman , S. Suwanto and W.A. Din
  A perpetuation from previous studies, it aims to fit a nonlinear mathematical model, specifically the modified Gompertz Model into a data involving language learning strategies. These language learning strategies are regarded as the six independent variables. Whereas, the language proficiency is regarded as the dependent variable. The language proficiency is measured according to the student’s Malaysian University English test result where two hundred and thirty pre-university students of Universiti Malaysia Sabah participated. These language learning strategies are based upon a self-report questionnaire called the strategy inventory for language learning. The model’s goodness-of-fit was tested using Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Residual Standard Error (RSE).
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