Australian Institute of High Energetic Materials ABN: 68 126 426 917
[Workshop Number]
[Computational Numerical Methods for Engineers] Workshop for Intensive Professional Development of Engineers and Technologists
Workshop Guide [Year] © Australian Institute of High Energetic Materials, [year].
This Workshop Guide was prepared by: [Dr. P. Balasubramanian] [Assistant Professor, Indian Institute of Technology Guwahati] [Department of Chemical Engineering, IIT Guwahati, Guwahati, India] and approved for distribution by: Dr V. Stamatov Director of the Australian Institute of High Energetic Materials Melbourne, Australia
This Workshop Guide was Produced and Published by: Australian Institute of High Energetic Materials ABN: 68 126 426 917 E-mail:
[email protected] Web: http://www.workshops.ausihem.org http://www.ausihem.org/workshop
First Published [month, year] Revised & Printed [month, year] © Copyright [year]
NOT FOR RESALE. All materials produced for this workshop are protected by copyright. Registered workshop participants/students are permitted to use these materials for personal study and research only, as permitted under the Copyright Act. Use of these materials for any other purposes, including copying or resale may infringe copyright unless written permission has been obtained from the copyright owners. Enquiries should be made to the publisher.
© Australian Institute of High Energetic Materials, [year].
Contact details Lecturer: Postal address:
E-mail:
Dr, Balasubramanian, Periyasamy Department of Chemical Engineering Indian Institute of Technolgy Guwahati Guwahati, Assam, 781039,India
[email protected]
Workshop Coordinator: Phone: Fax: E-mail:
Brief Curriculum Vitae of the Lecturer Periyasamy Balasubramanian born on June 10, 1975 at Then Pasiyar, India. He completed his Bachelor’s degree in Chemical Engineering at Coimbatore Institute of Technology, Coimbatore in 1997, and master degree in Petroleum Refining and Petrochemicals at Anna University, Chennai in 1999. He was awarded Doctoral degree in Chemical Engineering by the Indian Institute of Technology Madras in 2004 for his thesis entitled “Modeling and Simulation of Hydrocracking Process”. He worked as a postdoctoral fellow at LPT, Ghent University, Belgium for about two years. Since 2007, the author is working as a faculty at Indian Institute of Technology Guwahati. The author has membership in the following professional societies: American Chemical Society (ACS), American Institute of Chemical Engineers (AIChE), and Indian Institute of Chemical Engineers (IIChE). Honorary fellow of Australian Institute of High Energetic Materials. His research interests are Reaction Engineering, Non-linear Bifurcation Analysis, and Petroleum Processing. He has published ten research articles in refereed journals.
© Australian Institute of High Energetic Materials, [year].
Content Workshop Outline ................................................................................................... 1 Workshop synopsis ............................................................................................... 1 Learning outcomes ................................................................................................ 1 Workload ............................................................................................................... 2 Workshop prerequisites ......................................................................................... 2 Continuous improvement ....................................................................................... 2 Teaching and Learning Method.............................................................................. 3 Workshop Resources ............................................................................................. 3 Prescribed text(s) and readings ............................................................................. 3 Workshop schedule ............................................................................................... 4
© Australian Institute of High Energetic Materials, [year].
Australian Institute of High Energetic Materials – W##/09 Workshop Guide
Workshop Outline Workshop synopsis The workshop on “Computational Numerical Methods for Engineers” is intended for young professionals to learn the computer program for the numerical methods to solve the engineering problems using SCILAB and MATLAB software. The former software is a freeware, and the latter is a licensed one. Students are advised to use any one of the software to write a computer program for the solution of linear and nonlinear equations, regression, differential equations, and so on. Each module of the course contains a description of the numerical methods in general, and in a mathematical context, through step-by-step instructions, numerous examples, and comprehensive explanations for each method, problem and computer program. This essential course features SCILAB and MATLAB programs, and acquaints students with the advantages of each tool.
Learning outcomes At the conclusion of the workshop, students will be able to:
1. learn the numerical methods for determining the solution of algebraic and differential equations. 2. acquaint the usage of SCILAB and MATLAB software packages for the solution of the engineering problems through computer aided numerical methods. 3. enhance the computational skills to write a general program for the numerical methods such as Newton-Raphson method, Runge-Kutta fourth order method, cubic splines, Cranck-Nicolson scheme, and so forth. 4. solve the real world engineering problems through computer aided numerical methods using the numerical computation software.
© Australian Institute of High Energetic Materials, [year].
Australian Institute of High Energetic Materials – W##/09 Workshop Guide
Workload Lectures
26 hours
Tutorials
14 hours
Assignments, tests
7 hours, 3 hours
Private study (Lecture revisions and additional research and reading)
nil
Total
50 hours
Workshop prerequisites Desirable: Computer programming using FORTRAN and C, Basic Numerical Methods Essential: Nil
Continuous improvement Australian Institute of High Energetic Materials strives for the highest possible quality in teaching and learning. To monitor how successful the Institute is in providing quality teaching and learning we regularly seek feedback from our students and staff. Feedback is welcome at any time throughout the duration of the workshop. A Workshop Evaluation Survey will be carried out at the end of the workshop. Students are strongly encouraged to complete the survey as it is important tool to improve the quality of teaching. The feedback is anonymous and provides the Institute with evidence of aspects that students are satisfied and areas that need improvement.
© Australian Institute of High Energetic Materials, [year].
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Australian Institute of High Energetic Materials – W##/09 Workshop Guide
Teaching and Learning Method The workshop consists of 26 hours of lectures followed by 14 hours of tutorials. Students are advised to study all the lectures to participate in the tutorial sessions. There will be an assignment to complete after each tutorial. These assignments will be marked at the end of the sessions, and every assignment will contribute 10 % to the final marks. A final 3 hours open book examination will be carried out at the end of the workshop. The final examination will contribute with 40 % to the final marks. Students must achieve an overall mark of 50 % or above to achieve a pass in the workshop.
Workshop Resources Prescribed text(s) and readings Steven C. Chapra, Raymond P. Canale, Numerical Methods for Engineers, McGraw Hill, 6th edition, 2010. Won Young Yang, Wenwu Cao, Tae- Chung, Sang Chung, John Morris, Applied Numerical Methods Using Matlab, John Wiley, 2005. John H. Mathews, Kurtis D. Fink, Numerical Methods Using MATLAB, Prentice Hall, 4th Edition, 2003. Alkis Constantinides, Navid Mostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications, Prentice Hall,1999.
© Australian Institute of High Energetic Materials, [year].
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Australian Institute of High Energetic Materials – W##/09 Workshop Guide
Workshop schedule No 1
2
Lecture Introduction to Scilab and Matlab programming
Tutorial Problem solving using Scilab and Matlab software.
Duration: 1 hour
Duration: 1 hour
Numerical solution of system of linear Equations
Computer programs for the following numerical methods using Scilab and Matlab software are to be provided followed by illustrative examples.
-
Gaussian elimination
-
Gauss-Jordan method
-
LU decomposition: Doolittle, Crouts, and Cholesky
-
Jacobi’s and Gauss-Seidel iterative methods
Problems: Engineering problems Duration: 4 hour
3
4
Numerical solution of nonlinear equations -
Bracketing methods
-
Newton-Raphson method: Single variable and multivariable methods
-
Secant method
-
Muller’s method
-
Gaussian elimination method
-
Doolittle method
Exercises Duration: 2 hour Assignment 1: Write a computer program for the following numerical methods: -
Gauss-Jordan method
-
Gauss-Seidel iterative method
Computer programs for the following numerical methods using Scilab and Matlab software are to be provided followed by illustrative examples. -
Bisection method
-
Single variable NewtonRaphson method
Exercises
Problems: Engineering problems
Duration: 2 hour
Duration: 4 hour
Assignment 2: Write a computer program for the following numerical methods using SCILAB software:
Curve fitting -
Regression: Method of least squares
-
Linear regression
-
Multiple linear regression
-
Multivariable Newton-Raphson method
-
Muller’s method
Computer programs for the following numerical methods using Scilab and Matlab software are to be provided followed by illustrative examples -
Linear regression
-
Lagrange interpolation
© Australian Institute of High Energetic Materials, [year].
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Australian Institute of High Energetic Materials – W##/09 Workshop Guide -
Nonlinear regression
Exercises
-
Interpolation:
Duration: 2 hour
-
Linear interpolation
-
Lagrange interpolation
Assignment 3: Write a computer program for the following methods using SCILAB software.
-
Newton interpolation
-
Cubic splines
-
Multiple linear regression
-
Cubic splines with the natural and clamped end conditions
Problems: Engineering problems Duration: 4 hour 5
6
Eigenvalue problems -
Characteristic polynomial
-
Power method
-
Shifted inverse power method
-
Jacobi’s method
-
Power method
Exercises
Problems: Engineering problems
Duration: 1 hour
Duration: 2 hour
Assignment 4: Write a computer program for the Jacobi’s method using SCILAB package.
Ordinary differential equations: IVP
Computer programs for the following numerical methods using Scilab and Matlab software packages are to be provided followed by illustrative examples
-
Numerical differentiation
-
Numerical Integration
-
Euler’s method
-
Heun’s method
-
Numerical differentiation
-
Runge-Kutta second order and fourth order method
-
Numerical Integration
-
Euler’s method
-
Stiff differential equations
-
Nonlinear shooting method
-
Multistep methods
Ordinary differential equations: BVP -
Shooting methods
-
Finite differences
Problems: Engineering problems Duration: 6 hour
7
Computer programs for the following numerical method using Scilab and Matlab software are to be provided followed by illustrative examples
Partial Differential Equations -
Method of lines (finite
Exercises Duration: 3 hour Assignment 5: Write a computer program for the following numerical method. -
R-K fourth order method for the system of simultaneous differential equations
-
Multistep methods
-
Finite differences
A computer program for the solution of the parabolic partial differential
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Parabolic equations
-
Elliptic equations
-
Hyperbolic equations
-
Advances in differential equations
equations using explicit finite difference approximations is to be provided followed by the illustrative examples. Computer program for the O Brien et al. implicit method (heat equation) . Exercises
-
Integral-differential equations
Duration: 3 hour
-
Differential-Algebraic equations
-
Delay differential equations
Assignment 6: Write a computer program for the Cranck Nicolson method using SCILAB package.
Problems: Engineering problems Duration: 5 hour
Write a computer program for the solution a hyperbolic PDE.
© Australian Institute of High Energetic Materials, [year].
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