One of the purposes of this course is to provide the basic techniques for the numerical resolution of EDPs. To do this end, we will analyze and establish the theoretical properties of each method (stability, precision, computational complexity) and we will demonstrate its operation with examples that describe its advantages and disadvantages. The main objective is to develop algorithmic thinking, emphasizing the main computational concepts.
More specifically, the aims of the course with respecty to the students include:
- Understanding of main numerical approximation methods for PDEs: finite difference method; finite element method; spectral methods for periodic and non-periodic problems.
- Ability to analyze the main features of a numerical method: order, stability, convergence.
- Ability to implement numerical methods for the solution of PDEs in one and two dimensions.
- Have criteria to assess and compare different methods depending on the problems to be solved, the computational cost and the presence of errors.
- Ability to program the algorithms studied in the course or use previously programmed algorithms (for example, in Matlab or Python).
CB6, CB7, CB8, CB9, CB10
CG1, CG2, CG3, CG4, CG5, CG6, CG7
CE1, CE2, CE3, CE4, CE5, CE6, CE8, CE9, CE10, CE11, CE12, CE13