At the end of the course,
- You will be able to employ a range of techniques to approximately solve partial differential equations when exact methods cannot be applied.
- You will be able to analyze finite difference schemes for linear partial differential equations and determine their convergence, accuracy, stability, and relative efficiency.
- You will be able to convert a finite difference algorithm into a well-designed code in Python. You will know how to test (verify) a numerical simulation code.
This numerical analysis course is concerned with the approximate solutions of partial differential equations (PDEs), which are important in mathematical modeling in all fields of science and engineering. In the real world (i.e., outside university), analytic methods can rarely be applied to give quantitative results, so numerical methods are essential. We will focus mainly on the Finite difference methods for solving PDEs and combine learning about their mathematical aspects, such as accuracy and stability, with their practical implementation using Python.
Previous knowledge of PDEs and Numerical Methods for ODEs is helpful. The course can be followed without having this background knowledge, but additional self-study is recommended for a deeper understanding of the material.
Exam, which carries 80% of the final grade and will be written or oral depending on the number of participants, and a coding project, which carries 20% of the final grade.