MTH4340 Numerical methods for partial differential equations

When you finish this unit, you should be able to:

1. 1

   Critically evaluate and articulate the necessity of numerical methods for obtaining quantitative information on the solutions to partial differential equations;

2. 2

   Design, analyse, and rigorously assess the convergence and stability of numerical methods for a wide range of partial differential equations, demonstrating a deep understanding of the underlying mathematical principles;

3. 3

   Select and justify the use of advanced discretisation techniques based on their specific characteristics and the features of the considered mathematical model, showcasing expertise in tailoring methods to complex problems;

4. 4

   Implement advanced numerical methods in high-level programming languages such as Python or Julia, and critically interpret and analyse the resulting numerical outputs, demonstrating proficiency in computational skills;

5. 5

   Communicate complex theoretical and practical numerical problems involving partial differential equations with clarity and precision, both in written and oral forms, suitable for academic and professional audiences.