2.7 Exercises

2.01 Upwind differences.

2.02 Numerical dispersion.

2.03 Shock waves using Lax-Wendroff.

2.04 Leapfrog resonator.

2.05 European option.

2.06 Particle in a periodic potential.

2.07 Lax-Friedrichs advection.

2.08 Electromagnetic waves.

These problems can be edited / submitted for correction from your web browser by selecting assignments under the course main page. The color coding corresponds to the level of difficulty / amount of work:

Easy (2-4 hours).

The problem is a direct illustration of the syllabus and highlights a particular aspect of the theory: the solution consists of a short text with explanations, formulas, maybe an ASCII plot or sometimes a simple modification of the JBONE applet.

Moderate (1 day).

The problem deals with an extension of the syllabus or an application: the solution combines all the steps, starting from the formulation of a model, the analytical derivation of a numerical scheme, the implementation of a program and finishing with a discussion of the simulation in the JBONE applet.

Difficult (2-3 days).

The problem describes an application from a neighbouring field that goes beyond the scope of this course, but can be examined to open the scientific horizon: a certain degree of independence and creativity are required to outline a certain aspect, solve the equations and discuss the result.

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