Many real-world problems are formulated in terms of differential equations for which explicit solutions do not exist. Therefore, it becomes necessary to implement numerical methods to approximate the solutions of these problems. In this course, we will explore classical numerical methods for solving both ordinary and partial differential equations (with particular interest in the finite element method). By studying these methods, students will gain the skills needed to tackle a wide range of practical problems in fields such as physics, engineering, and biology.
Some of the topics studied in this course are the following:
Part I : Numerical methods for ordinary differential equations
One step methods
Multi step methods
Consistency, Stability and Convergence
Part II: Numerical methods for partial differential equations
Hilbert spaces, weak derivatives
Weak formulation an existence and uniqueness of solutions
The Galerkin method
The finite element method
Time dependent problems
- verantwortliche Lehrperson: Josué Daniel Diaz Avalos
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