Description and aims :

The course deals with the numerical solution of differential equations and systems of non-linear equations.

Content :
The content of this course consists of the following topics: Numerical Solution of ODE: Euler Methods, Heun’s Method, Runge Kutta Methods, System of ODE, Boundary Value Problems, Finite Difference Methods, Numerical Solution of PDE: Parabolic, Hyperbolic, and Elliptic Partial Differential Equations

Learning Objectives

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge
The student
• has knowledge of state-of-the-art numerical methods in the field.
• knows the convergence conditions for the different methods.
• knows which order the different methods have and what exactly the term order means.
• understands the concept of the stability domain for the different numerical schemes.
• knows finite differences for ODE and PDE.
• simulates the ODE and PDE.
• applies the schemes to real life problems.
• writes a numerical paper.
• presents the self-learning materials.

Skills
The student
• is able to use the methods in numerical calculations. That is; to be able to implement them on a computer.
• is able to analyze the order of a numerical method.
• understands the possibilities and the limitations of the different methods