Get the complete project »
- The Complete Research Material is averagely 52 pages long and it is in Ms Word Format, it has 1-5 Chapters.
- Major Attributes are Abstract, All Chapters, Figures, Appendix, References.
- Study Level: BTech, BSc, BEng, BA, HND, ND or NCE.
- Full Access Fee: ₦4,000
This project describes a differential equation of radioactive decay is numerically solved using the fourth order Runge-Kutta method. In order to properly estimate the quality of such methods, knowledge of the accuracy of the decay simulation is required. Here we consider the use of an EXCEL spreadsheet to tackle these drawbacks. In doing so, we employ the concept of relative row, relative column and fixed column in the spreadsheet to obtain the solution of systems of ODEs by the RK4 method. it is found that the way suggested here is faster than applying a scientific calculator and the solution obtained is significantly more accurate. I have numerically obtained the number of undecayed nuclei as a function of time. I haved displayed the numerical values graphically as well as in the form of data tables.
Numerical solutions to engineering or science problems have historically been carried out using procedural programming languages. This is not efficient from a pedagogical perspective because students typically must put more effort into learning the language itself than they put into solving problems (Qureshi et al., 2013). For example, the numerical solution of a boundary value problem in one dimension using finite difference techniques generally involves the creation of a system of linear equations and the conversion of that system into an equivalent matrix equation that then can be solved. Many students find this process confusing, so, for instance, a simple change such as modifying the boundary conditions often takes substantial effort to incorporate into a working solution.
The difficulty here is that students become bogged down in forcing the algorithm to fit a structure required by the procedural language, rather than implementing the change in a more natural way. Modern computational tools can alleviate this difficulty, easing the programming effort required and allowing students to spend more time focusing on the performance of the algorithms and on the behavior of the resulting solutions (Chandio and Memon, 2010). Students are able to implement algorithms in a more convenient format, removing some of the steps typically required in reaching a solution and thus allowing more effort to be spent comparing various algorithms and studying the behaviors of the equations themselves (Abraham, 2007).
One example of a tool with which equations are easily solved is the spreadsheet,which is particularly well-suited to the numerical solution of both differential and integral equations.
There are many physics problems that involve first order Odes. For example resistance, inductances, electrical circuits and radioactive decays (Boyce and DiPrima, 2001). Ordinary differential equations also appear in numerous problems in population biology and engineering giving mathematical descriptions of some phenomena. The numerical analysis of differential equations describes the mathematical background for understanding numerical methods giving information on what to expect when using them.
For studying numerical methods as a part of a more general course on differential equations, many of the basic ideas of the numerical analysis of differential equations are tied closely to theoretical behavior associated with the problem being solved (Glaser and Rokhlin, 2009). Differential equations can describe nearly all systems undergoing change and are essential parts of many areas of mathematics, from fluid dynamics to celestial mechanics. They are used by mathematicians, physicists and engineers to help in the designing of everything from bridges to ballistic missiles.
Ordinary Differential Equations (ODEs) are one of the most important and widely used techniques in mathematical modeling. However, not many ODEs have an analytic solution and even if there is one, usually it is extremely difficult to obtain and it is not very practical ( Amen et. al., 2004).
1.2 AIM AND OBJECTIVES OF STUDY
To solve the radioactive decay equation numerically using the runge-kutta algorithm and compare same with its analytical solution.
The specific learning objectives are:
(a) To develop a microsoft excel code to implement the RK4 algorithm for the radioactive decay equation.
(b) To plot the numerical solution side-by-side the analytical solution.
(c) To compare graphically relationship between the analytical and the numerical solutions.
The limitation of analytical techniques to solve the nonlinear differential equations has impeded the use of numerical methods for obtaining an approximate solution of the problem (Garewal, 2000).
You either get what you want or your money back. T&C Apply
You can find more project topics easily, just search
SIMILAR PHYSICS FINAL YEAR PROJECT RESEARCH TOPICS
1. A STUDY ON THE COMPETENCY OF PHYSICS STUDENTS IN THE USE OF INFORMATION COMMUNICATION TECHNOLOGY A CASE STUDY OF UNIVERSITY OF BENIN» ABSTRACT This study investigates the competency of physics students in the use of information and communication technology in University of Benin (UNI...Continue Reading »
2. ASSESSMENT OF RADIO-FREQUENCY RADIATION EXPOSURE FROM SELECTED MOBILE BASE STATIONS IN ZARIA AND ENVIRONS, NIGERIA» ABSTRACT Base transceiver stations (BTS) or mobile base stations produce non ionizing (RF) energy that is radiated through its antennas into space. Th...Continue Reading »
3. EFFECTIVE COMMUNICATION BETWEEN RADIOGRAPHERS AND PATIENTS: INFLUENCE ON SERVICE DELIVERY AND PATIENT SATISFACTION.» CHAPTER ONE 1.0 INTRODUCTION 1.1 BACKGROUND OF STUDY Communication is vital to good patient care in any discipline in the health domain and there is a...Continue Reading »
4. THE ASSESSMENT ON THE IMPLEMENTATION OF SECONDARY SCHOOL PHYSICS SYLLABUS A CASE STUDY OF ABEOKUTA SOUTH LOCAL GOVERNMENT AREA ABEOKUTA OGUN STATE» ABSTRACT It is a well know fact that the act of learning and teaching of physics among secondary school students has been deteriorated to the extent t...Continue Reading »
5. ASSESSMENT OF OCCUPATIONAL EXPOSURE AND RADIATION PROTECTION IN SOME SELECTED WELL-LOGGING AND INDUSTRIAL RADIOGRAPHY FACILITIES IN NIGERIA» ABSTRACT Nigeria has for a very long time engaged in the peaceful application of nuclear technology. The use of ionizing radiation due to its unique p...Continue Reading »
» CHAPTER ONE INTRODUCTION 1.1 INTRODUCTION Fuel burn up was shown to be linearly dependent on the reactor thermal power (Podvratnik, 2011). It is there...Continue Reading »
» ABSTRACT This project is a construction of a module of a zener diode and how output voltage varies with increase in current in forwards bias using mil...Continue Reading »
» ABSTRACT This work on ”Possible effects of Electromagnetic Fields (EMF), Radio Frequency Fields (RF) and Microwave Radiation on human health&rdq...Continue Reading »
9. ELEMENTAL ANALYSIS OF LIQUID WASTE GENERATED BY BRITISH AMERICAN TABACCO COMPANY USING INSTRUMENTAL NEUTRON ACTIVATION ANALYSIS (INAA) TECHNIQUES» CHAPTER ONE 1.1 INTRODUCTION Environment is a surrounding atmosphere or condition for existence. Some environment are cleaner than others and that is ...Continue Reading »
» ABSTRACT This study is undertaken to measure the variation of terrestrial gamma radiation and the activity concentrations of U 238, Th 232 and K 40 in...Continue Reading »