ME710 HIGHER ORDER NUMERICAL METHODS FOR PARTIAL DIFFERONTIAL EQUATIONS
| Course Code: | 5690710 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mechanical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. IŞIK HAKAN TARMAN |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course aims to instill/promote the following knowledge, behaviors and skills in the students
1. Fourier and Polynomial (Chebyshev) approximation of functions
2. Collocation aproach for solving differential equations based on Fourier and Polynomial (Chebyshev) bases
3. Variational aproach for solving differential equations based on Fourier and Polynomial (Legendre) bases
Course Content
Introduction to the concept of spectral methods. Fourier-collocation spectral methods. Polynomial-collocation spectral methods. Smoothness and accuracy. Boundary value problems. Polar coordinates. Time stepping. Initial value problems. Introduction to spectral element method and Discontinuous Galerkin method.
Course Learning Outcomes
At the end of this course, the students will be able to 1. Use Fourier and Polynomial expansions to approximate functions. 2. Use Collocation method based on Fourier and Poynomial (Chebyshev) expansion functions to solve differential equations. 3. Use Variational methods (Spectral Element, Discontinuous Galerkin) based on Fourier and Poynomial (Legendre) expansion functions to solve differential equations. 4. Understand the concepts of accuracy, consistency and stability of linear multistep methods of discretizing ODEs. 5. Understand the concepts of Stiffness, Condition and Preconditioning. 6. Develop Matlab codes to implement the numerical techniques introduced.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Acquires the fundamental scientific knowledge required to analyze and solve advanced-level problems in the field of mechanical engineering. | ✔ | |||
| 2 | Gains the competence to utilize advanced engineering mathematics methods in the formulation, analysis, and solution of engineering problems. | ✔ | |||
| 3 | Conducts literature reviews using printed and online sources, analyzes the collected literature, and identifies the current state-of-the-art in the relevant scientific field. | ✔ | |||
| 4 | Demonstrates the ability to prepare and deliver a seminar on a technical subject. | ✔ | |||
| 5 | Develops the ability to conduct independent research on a specific topic and solve advanced engineering problems. | ✔ | |||
| 6 | Contributes to the national and/or international body of knowledge through original research. | ✔ | |||
| 7 | Gains the competence to effectively communicate the process and results of research conducted on a specific subject through scientifically structured written reports and oral presentations. | ✔ | |||
| 8 | Acquires the ability to publish research findings as articles in national and/or international scientific journals and/or present them as papers at conferences. | ✔ | |||
| 9 | Acts in accordance with universal principles of research and publication ethics. | ✔ | |||