ES510 NUM. SOLUTION OF ORDINARY DIFF.EQUATION
| Course Code: | 5610510 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Engineering Sciences |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. MEHMET POLAT SAKA |
| Offered Semester: | Fall Semesters. |
Course Objectives
This course aims at covering advanced methods of numerical analysis. It briefs introduction to numerical computing, approximation and errors which is followed by methods of solving system of nonlinear equations and approximation of functions. Numerical solutions of ordinary differential equations; initial value problems and boundary value problems, simultaneous differential equations, Runga-Kutta methods, finite difference method. Numerical solution techniques for linear, elliptic, parabolic and hyperbolic partial differential equations. Methods will be implemented using toolboxes of MATLAB.
Course Content
Numerical solution of initial value problems: multi-step methods and Runge-Kutta methods, stability and convergence. Numerical solution of boundary value problems: shooting methods, finite difference and collocation methods, Green's function methods, transform methods, introduction to the finite element method. Nonlinear boundary problems.
Course Learning Outcomes
- To enable students to formulate mathematical modeling of engineering design problems
- To enable students to obtain the solution of nonlinear system of equations using numerical methods
- To enable students to use advanced curve fitting and interpolation methods to express any engineering data through Matlab tools
- To enable students to solve ordinary differential equations using numerical methods and Matlab tools
- To enable students to solve partial differential equation by using finite difference methods and Matlab tools.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Skills to analyse and to use different experiment set ups | ✔ | |||
| 2 | Skills to apply mathematical models to experimental and observatory results | ✔ | |||
| 3 | Ability to write and present research outcomes | ✔ | |||
| 4 | Awareness of academic and research ethics | ✔ | |||
| 5 | Ability to work in multidisciplinary groups | ✔ | |||
| 6 | Skills to follow new developments in basic science and engineering areas | ✔ | |||