To provide an introduction to the main topics of Numerical Analysis of Differential Equations with the central theme on the solution of initial, boundary and initial-boundary value problems of ordinary and partial differential equations. To practice the use of AI in computer implementation of the numerical algorithms, and be able to check the correctness, analyze the efficiency and iterate.
A. Apply and analyze numerical methods for initial value problems. B. Apply and analyze numerical methods for boundary value problems. C. Apply and analyze numerical methods for initial-boundary value problems. D. Reflect on computational efficiency in terms of cost and accuracy. E. Deliver reliable numerical results through error analysis and convergence test.
The delivery of the module is driven by the projects, and consists of a series of lectures, seminars and tutorials. Each lecture aim at an overview of the problem and methods. The seminars are in versatile forms. First, the instructor can introduce the projects to be carried out, and hint on resources and tools. Second, the students can present their work in progress and discuss with the instructor and classmates. Third, expert guests can be invited to stimulate more ideas. The tutorials are two folded. First, the instructor can demonstrate the workflow, key techniques and tools. Second, the instructor can review the projects and give feedback to the students' work.