Displaying publications 1 - 20 of 45 in total

  1. Hafizudin Mohamad Nor, Amirah Rahman, Ahmad Izani Md. Ismail, Ahmad Abd. Majid
    MATEMATIKA, 2016;32(1):53-67.
    Homotopy continuation methods (HCMs) can be used to find the solutions
    of polynomial equations. The advantages of HCMs over classical methods such as the
    Newton and bisection methods are that HCMs are able to resolve divergence and starting
    value problems. In this paper, we develop Super Ostrowski-HCM as a technique to
    overcome the starting value problem. We compare the performance of this proposed
    method with Ostrowski-HCM. The results provide evidence of the superiority of Super
  2. Norhashidah Awang, Ng, Kar Yong, Soo, Yin Hoeng
    MATEMATIKA, 2017;33(2):119-130.
    An accurate forecasting of tropospheric ozone (O3) concentration is benefi-
    cial for strategic planning of air quality. In this study, various forecasting techniques are
    used to forecast the daily maximum O3 concentration levels at a monitoring station
    in the Klang Valley, Malaysia. The Box-Jenkins autoregressive integrated movingaverage
    (ARIMA) approach and three types of neural network models, namely, backpropagation
    neural network, Elman recurrent neural network and radial basis function
    neural network are considered. The daily maximum data, spanning from 1 January
    2011 to 7 August 2011, was obtained from the Department of Environment, Malaysia.
    The performance of the four methods in forecasting future values of ozone concentrations
    is evaluated based on three criteria, which are root mean square error (RMSE),
    mean absolute error (MAE) and mean absolute percentage error (MAPE). The findings
    show that the Box-Jenkins approach outperformed the artificial neural network
  3. Shazmeen Daniar Shamsuddin, Nurlyana Omar, Koh, Meng-Hock
    MATEMATIKA, 2017;33(2):149-157.
    It has come to attention that Malaysia have been aiming to build its own
    nuclear power plant (NPP) for electricity generation in 2030 to diversify the national
    energy supply and resources. As part of the regulation to build a NPP, environmental
    risk assessment analysis which includes the atmospheric dispersion assessment has to
    be performed as required by the Malaysian Atomic Energy Licensing Board (AELB)
    prior to the commissioning process. The assessment is to investigate the dispersion of
    radioactive effluent from the NPP in the event of nuclear accident. This article will focus
    on current development of locally developed atmospheric dispersion modeling code
    based on Gaussian Plume model. The code is written in Fortran computer language
    and has been benchmarked to a readily available HotSpot software. The radionuclide
    release rate entering the Gaussian equation is approximated to the value found in the
    Fukushima NPP accident in 2011. Meteorological data of Mersing District, Johor of
    year 2013 is utilized for the calculations. The results show that the dispersion of radionuclide
    effluent can potentially affect areas around Johor Bahru district, Singapore
    and some parts of Riau when the wind direction blows from the North-northeast direction.
    The results from our code was found to be in good agreement with the one
    obtained from HotSpot, with less than 1% discrepancy between the two.
  4. Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, Rossita Mohamad Yunus
    MATEMATIKA, 2017;33(2):159-163.
    Replicated linear functional relationship model is often used to describe
    relationships between two circular variables where both variables have error terms and
    replicate observations are available. We derive the estimate of the rotation parameter
    of the model using the maximum likelihood method. The performance of the proposed
    method is studied through simulation, and it is found that the biasness of the estimates
    is small, thus implying the suitability of the method. Practical application of the
    method is illustrated by using a real data set.
  5. Ahmad Fadly Nurullah Rasedee, Mohammad Hasan Abdul Sathar, Norizarina Ishak, Irneza Ismail, Musab Sahrim, Nur Ainna Ramli, et al.
    MATEMATIKA, 2017;33(2):165-175.
    Real life phenomena found in various fields such as engineering, physics,
    biology and communication theory can be modeled as nonlinear higher order ordinary
    differential equations, particularly the Duffing oscillator. Analytical solutions for these
    differential equations can be time consuming whereas, conventional numerical solutions
    may lack accuracy. This research propose a block multistep method integrated with a
    variable order step size (VOS) algorithm for solving these Duffing oscillators directly.
    The proposed VOS Block method provides an alternative numerical solution by reducing
    computational cost (time) but without loss of accuracy. Numerical simulations
    are compared with known exact solutions for proof of accuracy and against current
    numerical methods for proof of efficiency (steps taken).
  6. Hasan, Talaat I., Shaharuddin Salleh, Sulaiman, Nejmaddin A.
    MATEMATIKA, 2017;33(2):191-206.
    In this paper, we consider the system of Volterra-Fredholm integral equations
    of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve
    SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition,
    a few theorems and two new algorithms are introduced. They are supported by
    numerical examples and simulations using Matlab. The results are reasonably good
    when compared with the exact solutions.
  7. Tiaw, Kah Fookand, Zarina Bibi Ibrahim
    MATEMATIKA, 2017;33(2):215-226.
    In this paper, we study the numerical method for solving second order Fuzzy
    Differential Equations (FDEs) using Block Backward Differential Formulas (BBDF)
    under generalized concept of higher-order fuzzy differentiability. Implementation of
    the method using Newton iteration is discussed. Numerical results obtained by BBDF
    are presented and compared with Backward Differential Formulas (BDF) and exact
    solutions. Several numerical examples are provided to illustrate our methods.
  8. Sagir, Abdu Masanawa, Sathasivam, Saratha
    MATEMATIKA, 2017;33(1):1-10.
    In the recent economic crises, one of the precise uniqueness that all stock
    markets have in common is the uncertainty. An attempt was made to forecast future
    index of the Malaysia Stock Exchange Market using artificial neural network (ANN)
    model and a traditional forecasting tool – Multiple Linear Regressions (MLR). This
    paper starts with a brief introduction of stock exchange of Malaysia, an overview of
    artificial neural network and machine learning models used for prediction. System
    design and data normalization using MINITAB software were described. Training
    algorithm, MLR Model and network parameter models were presented. Best training
    graphs showing the training, validation, test and all regression values were analyzed.
  9. Mamuda, Mamman, Sathasivam, Saratha
    MATEMATIKA, 2017;33(1):11-19.
    Medical diagnosis is the extrapolation of the future course and outcome
    of a disease and a sign of the likelihood of recovery from that disease. Diagnosis
    is important because it is used to guide the type and intensity of the medication
    to be administered to patients. A hybrid intelligent system that combines the fuzzy
    logic qualitative approach and Adaptive Neural Networks (ANNs) with the capabilities
    of getting a better performance is required. In this paper, a method for modeling
    the survival of diabetes patient by utilizing the application of the Adaptive NeuroFuzzy
    Inference System (ANFIS) is introduced with the aim of turning data into
    knowledge that can be understood by people. The ANFIS approach implements the
    hybrid learning algorithm that combines the gradient descent algorithm and a recursive
    least square error algorithm to update the antecedent and consequent parameters. The
    combination of fuzzy inference that will represent knowledge in an interpretable manner
    and the learning ability of neural network that can adjust the membership functions
    of the parameters and linguistic rules from data will be considered. The proposed
    framework can be applied to estimate the risk and survival curve between different
    diagnostic factors and survival time with the explanation capabilities.
  10. Nazatulsyima Mohd Yazid, Kim, Gaik Tay, Wei, King Tiong, Yaan, Yee Choy, Azila Md Sudin, Chee, Tiong Ong
    MATEMATIKA, 2017;33(1):35-41.
    In this paper, the application of the method of lines (MOL) to the Forced
    Korteweg-de Vries-Burgers equation with variable coefficient (FKdVB) is presented.
    The MOL is a powerful technique for solving partial differential equations by typically
    using finite-difference approximations for the spatial derivatives and ordinary differential
    equations (ODEs) for the time derivative. The MOL approach of the FKdVB
    equation leads to a system of ODEs. The solution of the system of ODEs is obtained
    by applying the Fourth-Order Runge-Kutta (RK4) method. The numerical solution
    obtained is then compared with its progressive wave solution in order to show the
    accuracy of the MOL method.
  11. Pandiya, Ridwan, Ismail Mohd
    MATEMATIKA, 2017;33(1):43-54.
    In this paper, we propose a method how to manage the convergence of
    Newton’s method if its iteration process encounters a local extremum. This idea establishes
    the osculating circle at a local extremum. It then uses the radius of the
    osculating circle also known as the radius of curvature as an additional number of
    the local extremum. It then takes that additional number and combines it with the
    local extremum. This is then used as an initial guess in finding a root near to that
    local extremum. This paper will provide several examples which demonstrate that the
    proposed idea is successful and they perform to fulfill the aim of this paper.
  12. Maizon Mohd Darus, Haslinda Ibrahim, Sharmila Karim
    MATEMATIKA, 2017;33(1):113-118.
    A new method to construct the distinct Hamiltonian circuits in complete
    graphs is called Half Butterfly Method. The Half Butterfly Method used the concept
    of isomorphism in developing the distinct Hamiltonian circuits. Thus some theoretical
    works are presented throughout developing this method.
  13. Mohd Bakri Adam
    MATEMATIKA, 2017;33(1):21-34.
    The constraint of two ordered extreme minima random variables when one
    variable is consider to be stochastically smaller than the other one has been carried
    out in this article. The quantile functions of the probability distribution have been
    used to establish partial ordering between the two variables. Some extensions and
    generalizations are given for the stochastic ordering using the important of sign of the
    shape parameter.
  14. Ummu Atiqah Mohd Roslan
    MATEMATIKA, 2018;34(1):13-21.
    Markov map is one example of interval maps where it is a piecewise expanding
    map and obeys the Markov property. One well-known example of Markov map is the
    doubling map, a map which has two subintervals with equal partitions. In this paper, we
    are interested to investigate another type of Markov map, the so-called skewed doubling
    map. This map is a more generalized map than the doubling map. Thus, the aims of this
    paper are to find the fixed points as well as the periodic points for the skewed doubling
    map and to investigate the sensitive dependence on initial conditions of this map. The
    method considered here is the cobweb diagram. Numerical results suggest that there exist
    dense of periodic orbits for this map. The sensitivity of this map to initial conditions is
    also verified where small differences in initial conditions give different behaviour of the
    orbits in the map.
  15. Gorgey, Annie, Nor Azian Aini Mat
    MATEMATIKA, 2018;34(1):1-2.
    Symmetric methods such as the implicit midpoint rule (IMR), implicit trapezoidal
    rule (ITR) and 2-stage Gauss method are beneficial in solving Hamiltonian problems
    since they are also symplectic. Symplectic methods have advantages over non-symplectic
    methods in the long term integration of Hamiltonian problems. The study is to show
    the efficiency of IMR, ITR and the 2-stage Gauss method in solving simple harmonic
    oscillators (SHO). This study is done theoretically and numerically on the simple harmonic
    oscillator problem. The theoretical analysis and numerical results on SHO problem
    showed that the magnitude of the global error for a symmetric or symplectic method
    with stepsize h is linearly dependent on time t. This gives the linear error growth when
    a symmetric or symplectic method is applied to the simple harmonic oscillator problem.
    Passive and active extrapolations have been implemented to improve the accuracy of the
    numerical solutions. Passive extrapolation is observed to show quadratic error growth
    after a very short period of time. On the other hand, active extrapolation is observed to
    show linear error growth for a much longer period of time.
  16. Keong, Ang Tau
    MATEMATIKA, 2018;34(1):143-151.
    In this paper we consider a harvesting model of predator-prey fishery in which
    the prey is directly infected by some external toxic substances. The toxic infection is
    indirectly transmitted to the predator during the feeding process. The model is a modified
    version from the classic Lotka-Volterra predator-prey model. The stability and bifurcation
    analyses are addressed. Numerical simulations of the model are performed and bifurcation
    diagrams are studied to investigate the dynamical behaviours between the predator and
    the prey. The effects of toxicity and harvesting on the stability of steady states found in
    the model are discussed.
  17. Chai, Jin Sian, Hoe, Yeak Su, Ali H. M. Murid
    MATEMATIKA, 2018;34(2):0-0.
    A mathematical model is considered to determine the effectiveness of disin-
    fectant solution for surface decontamination. The decontamination process involved the
    diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing
    effect. The mathematical model is a reaction-diffusion type. Finite difference method and
    method of lines with fourth-order Runge-Kutta method are utilized to solve the model
    numerically. To obtain stable solutions, von Neumann stability analysis is employed to
    evaluate the stability of finite difference method. For stiff problem, Dormand-Prince
    method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB
    programming is selected for the computation of numerical solutions. From the results
    obtained, fourth-order Runge-Kutta method has a larger stability region and better ac-
    curacy of solutions compared to finite difference method when solving the disinfectant
    solution model. Moreover, a numerical simulation is carried out to investigate the effect
    of different thickness of disinfectant solution on bacteria reduction. Results show that
    thick disinfectant solution is able to reduce the dimensionless bacteria concentration more
  18. Suhartono, Prastyo, Dedy Dwi, Kuswanto, Heri, Muhammad Hisyam Lee
    MATEMATIKA, 2018;34(1):103-111.
    Monthly data about oil production at several drilling wells is an example of
    spatio-temporal data. The aim of this research is to propose nonlinear spatio-temporal
    model, i.e. Feedforward Neural Network - VectorAutoregressive (FFNN-VAR) and FFNN
    - Generalized Space-Time Autoregressive (FFNN-GSTAR), and compare their forecast
    accuracy to linearspatio-temporal model, i.e. VAR and GSTAR. These spatio-temporal
    models are proposed and applied for forecasting monthly oil production data at three
    drilling wells in East Java, Indonesia. There are 60 observations that be divided to two
    parts, i.e. the first 50 observations for training data and the last 10 observations for
    testing data. The results show that FFNN-GSTAR(11) and FFNN-VAR(1) as nonlinear
    spatio-temporal models tend to give more accurate forecast than VAR(1) and GSTAR(11)
    as linear spatio-temporal models. Moreover, further research about nonlinear spatiotemporal
    models based on neural networks and GSTAR is needed for developing new
    hybrid models that could improve the forecast accuracy.
  19. Kashif, Amber Nehan, Zainal Abdul Aziz
    MATEMATIKA, 2018;34(1):31-47.
    In this paper, Maxwell fluid over a flat plate for convective boundary layer
    flow with pressure gradient parameter is considered. The aim of this study is to compare
    and analyze the effects of the presence and absence of λ (relaxation time), and also the
    effects of m (pressure gradient parameter) and Pr (Prandtl number)on the momentum
    and thermal boundary layer thicknesses. An approximation technique namely Homotopy
    Perturbation Method (HPM) has been used with an implementation of Adam and Gear
    Method’s algorithms. The obtained results have been compared for zero relaxation time
    and also pressure gradient parameter with the published work of Fathizadeh and Rashidi.
    The current outcomes are found to be in good agreement with the published results.
    Physical interpretations have been given for the effects of the m, Pr and β (Deborah
    number) with λ. This study will play an important role in industrial and engineering
  20. Siti Mariam Norrulashikin, Fadhilah Yusof, Kane, Ibrahim Lawal
    MATEMATIKA, 2018;34(1):73-85.
    Simulation is used to measure the robustness and the efficiency of the forecasting
    techniques performance over complex systems. A method for simulating multivariate
    time series was presented in this study using vector autoregressive base-process. By
    applying the methodology to the multivariable meteorological time series, a simulation
    study was carried out to check for the model performance. MAPE and MAE performance
    measurements were used and the results show that the proposed method that consider
    persistency in volatility gives better performance and the accuracy error is six time smaller
    than the normal hybrid model.
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