MATH677 NUMERICAL METH. IN ORDINARY DIFF. EQU.
| Course Code: | 2360677 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. CANAN BOZKAYA |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will:
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understand the mathematical foundations and algorithmic structure of numerical methods for initial and boundary value problems
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analyze and implement single-step and multistep methods for solving ordinary differential equations (ODEs)
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study stiffness, stability, and convergence issues in numerical integration of differential equations
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apply and evaluate numerical techniques for solving both linear and nonlinear systems of ODEs
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explore structure-preserving methods such as those for Hamiltonian systems
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investigate numerical solutions of boundary value problems using various discretization strategies
Course Content
Introduction to Numerical Methods, Linear multistep methods. Runge-Kutta methods, stiffness and theory of stability. Numerical methods for Hamiltonian systems, iteration and differential equations.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
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classify and model initial value problems (IVPs) and boundary value problems (BVPs) arising in applied sciences and engineering
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implement and compare single-step methods (Euler, Taylor series, Runge-Kutta, implicit Runge-Kutta, extrapolation) for IVPs
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identify stiffness in ODE systems and select appropriate stable numerical solvers
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construct and apply multistep methods including predictor-corrector schemes; perform error and convergence analysis
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solve higher-order and coupled systems of ODEs using numerical discretization techniques
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apply numerical methods (finite difference, collocation, shooting) to boundary value problems
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analyze truncation errors, numerical stability, and convergence properties of the implemented algorithms
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develop and test numerical algorithms for solving time-dependent or structure-preserving systems, including Hamiltonian dynamics
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution