Proceedings of MUCET2010 Malaysian Technical Universities Conference on Engineering and Technology June 28-29, 2010, Bayview Hotel, Melaka, Malaysia MUCET2010
NUMCeE: NUMERICAL METHOD CALCULATOR FOR ENGINEERING EDUCATION. 1
Zuraini Othman, 2Dr Abdul Samad bin Shibghatullah
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Department of Industrial Computing, Faculty of Information and Communication Technology, Universiti Teknikal Malaysia Melaka, Malaysia. email:
[email protected],
[email protected]
needed for the solution of practical problems and they often require the systematic application of a range of elementary methods, often thousands or millions of times over ([5] [4]). In the development of numerical methods, simplifications need to be made to progress towards a solution: for example general functions may need to be approximated by polynomials and computers cannot generally represent numbers exactly anyway [6]. As a result, numerical methods do not usually give the exact answer to a given problem, or they can only tend towards a solution getting closer and closer with each iteration. Numerical methods are generally only useful when they are implemented on computer using a computer programming language [5].
Abstract— Numerical methods are the study of algorithms for the problems of continuous mathematics in different field including engineering education. The objective of numerical methods is the design and analysis of techniques to give approximate but accurate solutions to hard problems. Ways of computation of numerical methods are either manual or using mathematical software. Manual way of calculation is hard, takes time, and prone to error. Currently, there are mathematical software available in market such as MATLAB and Maple that are being used in engineering education. However, the limitations with the existing software are expensive, very general and not user-friendly. There are some commands that user needs to learn in order to generate the answer and different software had different command. It becomes difficult when the mathematical problem is complicated. Therefore, this research aims to produce mathematical engineering education software that is customized to specific need of students, lecturers, and researchers and more user-friendly. This paper presents the software (NUMCeE) that has been developed based on the survey[2] and to fulfill the research objective. NUMCeE is targeted to be used by students, lecturers and researchers in engineering field.
The learning and teaching of engineering is a challenging task for the students, lecturers and researchers[8]. The comprehension of difficult, mathematically formalized concepts can be greatly enhanced by the aid of high level simulation and visualization capabilities of numerical software, which can improve the learning efficiency by bringing to life the equations describing various physical phenomena ([5] [4]). The application of this kind of software in higher education makes it possible that engineering students gain a much deeper knowledge and understanding of any particular field of engineering, which they are interested in [7]. In addition, engineering students who usually not very involved in the detailed mathematical description of the solution of formally defined problems, a numerical software can help really a lot to understand problems of engineering and interpret their solutions in a visual, user-friendly environment ([5][7][4]). To the lectures it help them in educating the students by easily describe concepts through the visual, and easy to explain representation of the solutions. To the researchers it aids them to quickly understand and getting results to any problem related to numerical methods and guide them in choosing the best methods available.[3]
Keywords: Mathematical Software, Numerical Method, Engineering Education I.
Currently, there are mathematical software that support numerical methods available in market such as Matlab, Maple and Mathematica ([3][6]). However, the limitations with such software are that they are expensive, very general and not user-friendly [3].The license pricing is quite high and is not affordable to most of students, lecturers and researchers. Some of the commands users need to learn in order to generate the answer and different software had different command. It becomes difficult when the mathematical problem is complicated [6].
INTRODUCTION
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HE computer technology advancement has enabled many in science and engineering to apply numerical methods to simulate physical phenomena ([6][7]). Numerical methods are often divided into elementary ones such as finding the root of an equation, integrating a function or solving a linear system of equations to intensive ones like the finite element method. Intensive methods are often
This work was funded by FRGS grant by kementerian pendidikan tinggi malaysia. grant no FRGS/2007/FTMK(4)-F0051
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Percent of relatives error
Therefore, this research aims to produce numerical methods software for engineering education that is customized to specific need of students, lecturers, and researchers. The software will be affordable, more userfriendly, and easy to learn. However, prior to develop the software a survey is carried out to the specific users in order to identify the most mathematical problem and numerical methods they used, the limitations with current mathematical software package, and requirements for good mathematical software. The results of the survey were presented in [2]. The results suggest that a good mathematical software must has good features like user friendly, easy to use, cover all mathematical problems and simply touch one button to get the answer. Based on the finding, then NUMCeE was developed. The next section discusses the details of NUMCeE.
iii. Solution of Nonlinear Equations Bisection method Simple fixed-point iteration Newton- Raphson method iv. Solution of Linear Systems
This paper has been organized as follows. The next section presents the details of NUMCeE including the modules that it has. The following section discusses the interface of NUMCeE and results. In the last section, conclusions and suggestions for further research are dealt with.
v.
Gaussian Elimination Gaussian Elimination with partial Pivoting. LU Decomposition Gauss-Seidel Method. Interpolation
Newton’s interpolating polynomial Langrange interpolating polynomial vi. Curve Fitting. Linear regression
II. NUMCeE’S SYSTEM
Polynomial regression
NUMCeE is numerical software tool which is specially design to fulfill engineering education especially in Universiti Teknikal Malaysia Melaka (UTeM) and it is design based on feedback from survey conducted by [2]. Main objective of this system is to help students, lecturers and engineers in their teaching, learning and work. This system can be use as their calculator in order to solve problems that involve numerical calculation. This system is totally used c# language on Visual Express C# 2008 platform and it is comes with user friendly interface. By using this system users can see the details of calculation involve like iteration and they can view the graph involve on certain chapters. In order to fully utilize this system on teaching and learning, it is portable which can be carrying anywhere and also can be run in any Windows operating system. It is also comes with notes from the book which written by [1].
IV. INTERFACE AND RESULT NUMCeE is an application that can simulate some implementation of calculation in Numerical Method's subject. This application is small in size, portable which can be carrying anywhere and also can be run in any Windows operating system.
III. MODULE The module of this system is refer to the main UTeM student’s text book in numerical method which written by [1]. This system consist of six chapters of numerical methods subjects which are: i. Number System
Figure 1: Main Menu Figure 1 shows the main menu for NUMCeE. Each section have calculator application and own notes which can be as reference during simulation. User can see the applications and notes by expanding each chapter in the tree menu at left and double click on particular item.
Binary operation Converting number Floating-point numbers ii. Error Absolute error Relatives error
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Figure 5: Error Figure 5 shows calculation on error which are absolute error relative error and percent of relative error. This calculation provides how much error between real value and approximation value.
Figure 2: Binary operation Figure 2 shows binary operation. Operations involve are addition, subtraction, multiplication and divide. In this calculation, we cannot type other number except 0 and 1 only.
Figure 3: Converting Number Figure 3 shows Converting number. It can be used to convert between binary number, decimal number, octal number, hexadecimal number and convert between binary faction to decimal fraction.
Figure 6: The solution of nonlinear equation Figure 6 shows calculation to find the root of equation by using three methods: Bisection. Simple fixed-point Newton Raphson By entering an equation x0 and x1, the application can display the result of iteration in table and give the answer or root for the equation.
Figure 4: Floating Point Figure 4 shows floating point section which can convert any fractional number into floating point number which is used inside the computer.
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Figure 7: Linear System Figure 7 shows linear system page, user can solve Linear System problem equation up to 6x6 matrix. There are four methods that can be used in this application: Gaussian Elimination Gaussian Elimination with partial Pivoting. LU Decomposition Gauss-Seidel Method.
Figure 9: Curve Fitting Figure 9 shows tool to plot a graph and it has ability to do Linear and Polynomial regression. It will display the final equation and the graph. V. FUTURE WORK AND CONCLUSION
This paper presents the modules in NUMCeE that has been developed based on the survey[2]. The modules are Number System, Error, Solution of Nonlinear Equations, Solution of Linear Systems, Interpolation, and Curve Fitting. The software is still in the process of development therefore the testing phase is not started yet. For the future work, functional testing and user acceptance testing will be conducted. Other than that this work will continue to design and develop another five chapters on [1]. NUMCeE is hoped to fulfill the requirements of students, lecturers and researchers in engineering field. REFERENCES [1]
Figure 8: Interpolation Figure 8 shows interpolation page, user can use this to estimate the value of a function for any intermediate value of the independent variable. This section can plot graph for user and user can see visually how their equation mapped in real world. There are 3 orders of calculation that can be used: Linear Quadratic Cubic User also can choose to use Newton's Interpolation or Lagrange Interpolation algorithm in calculation which gives the same result.
[2]
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[5]
[6]
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