

Articles
by
J. Sulaiman 
Total Records (
13 ) for
J. Sulaiman 





W. S. Koh
,
J. Sulaiman
and
R. Mail


Problem statement: Modified GaussSeidel (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 quartersweep iteration scheme, it can decrease the computational operations without altering the accuracy. In this study, we investigated the effectiveness of the new QuarterSweep Projected Modified GaussSeidel (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 quartersweep CrankNicolson 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 quartersweep algorithm based on Projected GaussSeidel (PGS) and Projected Modified GaussSeidel (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 GaussSeidel iteration from various grid sizes. Actually there were two types of linear models considered such as piecewise linear polynomial and piecewise RedlichKister 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 thirdorder RedlichKister polynomial has high accuracy compared to linear polynomial case. Conclusion: The efficiency of AM and GM iterative methods based on the RedlichKister 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 QuarterSweep Modified Successive OverRelaxation (QSMSOR) iterative method using cubic polynomial spline scheme for solving second order twopoint 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 FullSweep Modified Successive OverRelaxation (FSMSOR) and HalfSweep Modified Successive OverRelaxation (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 GaussSeidel (GS), FullSweep Successive OverRelaxation (FSSOR), HalfSweep Successive Over Relaxation (HSSOR) and QuarterSweep 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 FullSweep AGE (FSAGE) and HalfSweep 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 FullSweep 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 GaussSeidel (GS),
FullSweep AGE (FSAGE), HallSweep AGE (HSAGE) and QuarterSweep 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 TwoDimensional 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 1Dimensional Porous Medium
Equations (1D PMEs) using HalfSweep NewtonExplicit Group (HSNEG) iterative method. The general finite
difference approximation equation of 1D PME is formulated using the halfsweep 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 NewtonGaussSeidel (NGS) and
NewtonExplicit 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 collisionfree path from arbitrary start location to a specified end position in their environment. In this study, numerical technique, specifically on family of Accelerated OverRelaxation (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 finitedifference 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 preuniversity students of Universiti Malaysia Sabah participated. These
language learning strategies are based upon a selfreport questionnaire called the strategy inventory for
language learning. The model’s goodnessoffit was tested using Root Mean Square Error (RMSE), Mean
Absolute Error (MAE) and Residual Standard Error (RSE). 




A.A. Dahalan
,
W.K. Ling
,
A. Saudi
and
J. Sulaiman


Mobile robots have been undergoing constant research and development to improve its capability,
especially, in its ability plan its path and move to specified destination in a given environment. However, there
is much room for improvement of mobile robot path planning efficiency. This study attempts to improve the
path planning efficiency of mobile robots by solving the path planning problems iteratively by using numerical
method. This method of solution is based on harmonic function that applies the Laplace’s equation to control
the generation of potential function over the regions found in the mobile robot’s configuration space. This
study proposed the application of HalfSweep Modified Accelerated OverRelaxation (HSMAOR) iterative
method to solve the mobile robot path planning problem. By using approximation finite scheme, the experiment
was able to produce smooth path planning for the mobile robot to move from its starting point to its goal point.
Other than that, the experiment also shows that this numerical method of solving path planning problem is
faster and is able to produce smoother path for the mobile robot’s point to point movements. 





