MECH510 NUMERICAL METHODS IN ME II
| Course Code: | 3650510 |
| 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: | Masters |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course is intended to give graduate and senior-level undergraduate engineering students a foundation in the theory and methods for numerical solution of ordinary (ODEs) and partial differential (PDEs) equations. Topics include Runge-Kutta and multistep methods for single and systems of ODEs, shooting and finite difference methods for boundary value problems, numerical solution of linear second-order PDEs (Laplace, Poisson, heat and wave equations), advection and Burger's equations. Particular emphasis will be set on differences in solution methods for explicit and implicit numerical schemes as well as on establishing connection between their order, stability and convergence properties. Different relevant models from physics and engineering will be introduced and numerically solved.
Course Content
Ordinary differential equations. Euler, Runge-Kutta, multi-step, predictor-corrector methods. Boundary value problems. Matrix and shooting methods. Partial differential equations. Finite difference, Crank-Nicholson, Gauss-Seidel methods. (S)
Course Learning Outcomes
By the end of the course the students will be able to
- classify ODEs and PDEs
- tell the difference and relation between consistency, stability and convergence
- select an appropriate finite difference based numerical solution scheme for a given ODE or PDE
- code various implicit/explicit, single step/multi-step ODE solution schemes
- code various finite difference based schemes to solve elliptic, parabolic and hyberbolic PDEs
- perform stability analysis of various ODE and PDE solution schemes
- solve numerically some differential equatiions arising in real world applications