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
Ostrowski-HCM.
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.
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.
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).
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.
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.
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
methods.
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.
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.
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.
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.
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.
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.
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.
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.
In DNA splicing system, the potential effect of sets of restriction enzymes and
a ligase that allow DNA molecules to be cleaved and re-associated to produce further
molecules is modelled mathematically. This modelling is done in the framework of formal
language theory, in which the nitrogen bases, nucleotides and restriction sites are modelled
as alphabets, strings and rules respectively. The molecules resulting from a splicing system
is depicted as the splicing language. In this research, the splicing language resulting from
DNA splicing systems with one palindromic restriction enzyme for one and two (nonoverlapping)
cutting sites are generalised as regular expressions.
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.
Numerical simulation of the behaviour of blood flow through a stenosed bifurcated
artery with the presence of single mild stenosis at parent artery is investigated. The
flow analysis applies the incompressible, steady, three-dimensional Navier-Stokes equations
for non-Newtonian generalized power law fluids. Behaviour of blood flow is simulated
numerically using COMSOL Multiphysicsthat based on finite element method.The
results showthe effect of severity of stenosis on flow characteristics such as axial velocity
and its exhibit flow recirculation zone for analysis on streamlines pattern.
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.
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
applications.