EXECUTIVE SUMMARY PROPOSAL REPORT INTRODUCTION TO MATHEMATICAL MODELLING (MAT530) 2 nd AUGUST 2023 MATHEMATICAL SCIENCES STUDIES COLLEGE OF COMPUTING, INFORMATICS AND MATHEMATICS UNIVERSITI TEKNOLOGI MARA (UiTM) TERENGGANU BRANCH KUALA TERENGGANU CAMPUS
1 EXECUTIVE SUMMARY NAME AINA HAZIQAH BINTI ABDUL HAMID STUDENT ID 2020897442 TITLE COMPARISON of 4th ORDER RUNGE-KUTTA METHOD AND HEUN’S METHOD TO ESTIMATE JOHOR POPULATION IN 2023. SUPERVISOR DR. NUR ATIKAH BINTI SALAHUDIN Executive Summary. Numerical analysis is the mathematical material of scientific computing. Scientific computing also has been almost every problem reduces, at some level, to a problem in root-finding, a problem in nonlinear optimization, or a problem in numerical linear algebra, and that the first two cases frequently involve the solution of a linear system. This project, I will be used Heun method and 4th order Runge-Kutta to compare which one is the best method to estimates the population in Johor. The objective for this project is firstly to identify the equation of Verhulst model. Secondly, to determine the smaller percentage between both methods using MAPE. Lastly, to estimate the population of Johor state in 2023. For this project, to compare the best numerical method is by comparison the value error using MAPE.. The smallest error, mean the model is the best to estimate Johor population in 2023. EXECUTIVE SUMMARY NAME AMANINA BINTI ROZANI STUDENT ID 2021459696 TITLE OPTIMISING TRAFFIC SIGNALLING SYSTEM USING PARTICLE SWARM OPTIMISATION SUPERVISOR RUHANA BINTI JAAFAR Executive Summary. With the growing number of the world’s population, there is also an increase in the number of vehicles. This has led to the problem with traffic congestions especially at intersections equipped with traffic lights. An initiative to solve this issue would be to improve the traffic signalling system by optimising the cycle to minimise the delay of vehicles, reduce the total time of the vehicles’ journey, and to maximise the traffic capacity. Particle swarm optimisation (PSO) algorithm is to be employed to enhance the traffic control schemes. It is an algorithm inspired by the movement of particles in a swarm such as the movement of fish in a school, or birds in a flock. In an effort to produce an optimised cycle, different models of PSO will be applied and compared. The results will be displayed in graphs and charts and the best model will be selected.
2 EXECUTIVE SUMMARY NAME MUHAMMAD AMIR FARHAN BIN HASSAN STUDENT ID 2020847178 TITLE COMPARATIVE ANALYSIS OF NONLINEAR EQUATION SOLVERS: A STUDY ON NEWTON, OSTROWSKI, MODIFIED OSTROWSKI, STEFFENSEN, AND TWO-STEP STEFFENSEN METHODS SUPERVISOR DR. MOHD RIVAIE BIN MOHD ALI Executive Summary. Nonlinear equations are vital in scientific and engineering fields, representing relationships that deviate from simple linearity. Solving these equations is challenging but essential for optimization, modeling complex systems, and understanding physical phenomena. This research compares five numerical methods: Newton, Ostrowski, Modified Ostrowski, Steffensen, and Two-Step Steffensen, to solve nonlinear equations. The objectives are to find roots using these methods, analyze their efficiency in terms of iteration counts and execution times, and determine the best method for solving nonlinear equations. The research framework involves a literature review to understand the methods' strengths and limitations. Representative test functions with varying degrees of nonlinearity are selected. The methods are implemented using Maple 16 software, and experiments are conducted under different tolerance levels. The number of iterations required for convergence is recorded and analyzed to evaluate each method's performance. The findings will be discussed, considering convergence behavior, computational efficiency, and robustness. Recommendations for method selection and potential areas for further research will be provided. Expected findings include Newton's method demonstrating fast convergence near the solution but sensitivity to initial guesses. Steffensen's method is expected to achieve second-order convergence, while the Two-Step Steffensen method should exhibit fourth-order convergence, enhancing the convergence rate. Ostrowski's method, along with Modified Ostrowski methods, is anticipated to achieve higher convergence rates compared to the secant method. The modified versions are expected to offer enhanced efficiency and reduced function evaluations.
3 EXECUTIVE SUMMARY NAME MUHAMMAD ZAINULHAZIQ BIN ZAIDI STUDENT ID 2021614846 TITLE APPLYING ANT COLONY OPTIMIZATION TO SOLVE VEHICLE ROUTING PROBLEM SUPERVISOR SITI MUSLIHA BINTI NOR-AL-DIN Executive Summary. Complaints of inconvenient schedules, overpriced tickets, and lack of services are the reasons why individuals do not use buses as their daily transportation. So, the Vehicle Routing Problem (VRP) can be applied to overcome the issue by focusing on Rapid Kuantan. VRP involves determining the best route between two or more nodes in terms of total time, cost, and distance. The Ant Colony Optimization (ACO) algorithm can be used to address this problem. The goals of this study are to identify all possible routes for Rapid Kuantan, apply ACO to find the best route among the identified routes, and determine the best route that minimizes cost and travel time. These goals can be accomplished by conducting a Simulation of Urban Mobility (SUMO) to simulate the traffic network and acquire the results. The outputs will then be analyzed by ACO to generate a new value. The simulator will rerun the new value until the system has reached the desired level of optimization. The outcomes of each simulation will be compared among different algorithms with varying numbers of clients. Finally, by utilizing ACO, the optimal route that can minimize cost, maximize profit, and reduce passenger waiting time will be established.
4 EXECUTIVE SUMMARY NAME NURIN NADHIRAH BINTI IRMAN STUDENT ID 2021451302 TITLE MIXED CONVECTION FLOW OVER AN EXPONENTIALLY STRETCHING VERTICAL SURFACE IN SECOND-GRADE HYBRID NANOFLUID SUPERVISOR DR. SYAZWANI BINTI MOHD ZOKRI Executive Summary. Nanofluid is a suspension of nanometer-sized particles in a base fluid. The composition of two or more nanoparticles mixed in a base fluid, termed hybrid nanofluid has greater thermophysical properties than single-nanoparticle-type nanofluid. Second-grade fluid, a subcategory of non-Newtonian fluid, has become an intriguing topic of research due to its viscosity that can be altered by shear stress. The dispersion of nanoparticles into secondgrade fluid enhances the thermophysical properties, thus, becomes beneficial in the real-life scenarios as it can simulate the behavior of various applications in the industries of science, particularly engineering and thermal systems. Therefore, this study focuses on mixed convection flow over an exponentially stretching vertical surface in second-grade hybrid nanofluid. The similarity transformation variables will be applied to convert the partial differential equations (PDEs) into ordinary differential equations (ODEs). The governing ODEs obtained will be encoded in Maple software by employing the Runge-Kutta-Fehlberg Fourth Fifth (RKF45) method. The acquired results will then be validated by comparison with the findings of previous related studies. The outcome will be tabulated and graphically presented for skin friction coefficient, heat transfer coefficient, temperature profile, and velocity profile over pertinent parameters, namely Prandtl number, mixed convection parameter, stretching parameter, and second-grade fluid parameter. Practitioners in the industry can utilise the numerical solution achieved as a reference when conducting experiments in real-world situations.
5 EXECUTIVE SUMMARY NAME NURUL ASHIKIN BINTI SHAIPUDIN STUDENT ID 2020862176 TITLE UNSTEADY GRAVITY-DRIVEN RIVULET FLOW OF NEWTONIAN POWER-LAW FLUIDS WITH STRONG SURFACE-TENSION EFFECT SUPERVISOR DR NURUL AININA BINTI REDWAN Executive Summary. The study explores the behavior of thin fluid films flowing down inclined surfaces, commonly referred to as rivulet flows. The main focus is on the influence of power-law rheology and surface tension on the dynamics of these rivulet flows. The primary objective of this research is to gain a better understanding of the fundamental characteristics of unsteady rivulet flows with a Newtonian power-law fluid model, considering the effects of surface tension. The presence of power-law behavior in the fluid significantly affects the flow dynamics of rivulets. Strong surface tension at the fluid-air interface introduces unique phenomena, such as the formation of capillary waves and instabilities in the rivulet. These surface-tension-driven effects play a crucial role in determining the rivulet's shape and stability over time. The findings of this research have implications for various applications in science and engineering, including coating processes, microfluidics, and environmental studies. Understanding the dynamics of rivulet flows is essential for optimizing coating thickness in industrial processes and designing efficient microfluidic devices. Additionally, the insights gained from this study can aid in understanding similar phenomena occurring in natural environments, such as rainwater rivulets on inclined surfaces. The study on unsteady gravitydriven rivulet flow of Newtonian power-law fluids with strong surface-tension effects offers valuable insights into the complex behavior of thin fluid films. By considering the combined influence of power-law rheology and surface tension, researchers gain a deeper understanding of the underlying mechanisms governing rivulet dynamics. These findings contribute to the broader field of fluid mechanics and have practical applications in various industries and scientific disciplines.