Numerical Solution of Ordinary Differential Equations (AA5)
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Graduate Courses Outlines - Department of Mathematics
General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | AA5 |
Semester | 1 |
Course Title | Numerical Solution of Ordinary Differential Equations |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Numerical methods for initial value problems for ordinary differential equations are studied in this course; an introduction to numerical methods for the two-point boundary value problem is also given. Learning Objectives: Understanding the basic facts for initial value problems and the two-point boundary value problem. Understanding the fundamental qualitative characteristics of numerical methods for initial value problems, like consistency, order of accuracy, stability and convergence. It is expected that after taking the course the student will have:
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General Competences |
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Syllabus
- Short introduction to the theory of initial value problems.
- Analysis of the Euler methods: order of accuracy; stability properties, A-stability and B-stability; error estimates under various Lipschitz conditions (global, local and one-sided); a posteriori error estimates.
- Runge-Kutta and collocation methods: stability properties, order of accuracy, embedded pairs of methods and adaptive time step selection.
- Multistep methods: elements of the theory of difference equations, the root condition and stability, order of accuracy, one-leg methods, and G-stability.
- Introduction to the theory of the two-point boundary value problem: energy method and elliptic regularity.
- Finite difference methods for the two-point boundary value problem.
- Finite element method: construction of finite element spaces for various boundary conditions, Galerkin and Ritz methods, the Nitsche trick. Error estimates in the case of indefinite operators.
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