| CODE | MAT3772 | ||||||||||||
| TITLE | Numerical Methods for Differential Equations | ||||||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||||||
| MQF LEVEL | 6 | ||||||||||||
| ECTS CREDITS | 5 | ||||||||||||
| DEPARTMENT | Mathematics | ||||||||||||
| DESCRIPTION | 1) Numerical Methods for Initial value problems: - One-step methods, consistency and convergence; - Runge-Kutta methods; - Linear multistep methods, zero-stability and consistency; - Dahlquist’s theorems; - Systems of equations; - Stiff systems, Implicit Rung-Kutta methods. 2) Numerical Methods for Boundary value problems: - A model problem; - Error analysis; - Boundary conditions involving a derivative; - The general self-adjoint problem; - The Sturm Liouville eigenvalue problem. 3) The finite element method: - Galerkin weighted residual method; - Formulation of the finite element method; - Applications to boundary value problems. Study-Unit Aims: Numerical solution techniques for differential equations are a fundamental part of the applied mathematics. The unit emphasizes classical methods for finding approximate solution formulas. It also treats about quantitative information for error analysis of considered methods. These groups of methods can be classified as Initial Value Problems, Boundary Value Problems, and Finite Element Method. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - explain and interpret the concepts of consistency, convergence and stability of methods; - solve differential systems efficiently by various numerical techniques; - perform spacial discretization for different methods; - compare performance of the methods by error analysis. 2. Skills: By the end of the study-unit the student will be able to: - interpret and analyse the applicability and limitations of the methods; - compare the methods with error analysis; - solve linear differential equations by numerical calculations. Main Text/s and any supplementary readings: Main Texts: - E. Süli and D. Mayers. An introduction to Numerical Analysis. Cambridge University Press, 2003. Supplementary Readings: - K. W. Morton and D. F. Mayers. Numerical Solution of Partial Differential Equations, Cambridge University Press, 2005. - K. Atkinson, W. Han and D. E. Stewart. Numerical Solution of Ordinary Differential Equations. A john Wiley & Sons Inc., Publication, 2011. |
||||||||||||
| ADDITIONAL NOTES | Follows from: MAT3771 Leads to: MAT5713 |
||||||||||||
| STUDY-UNIT TYPE | Lecture, Independent Study and Project | ||||||||||||
| METHOD OF ASSESSMENT |
|
||||||||||||
| LECTURER/S | Onur Baysal |
||||||||||||
|
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
|||||||||||||