In this course a number of concrete differential equations are studied that arise in various fields from applied mathematics. The course discusses how the (ordinary, partial, stochastic) differential equation is derived and subsequently how it is converted into a numerical model. Important properties of this model are investigated. The distinctions and synergies between the various numerical methods will be emphasized, both theoretically and practically, via computer implementations. We discuss the predictions that can be made using the numerical models, and their importance to the applied field.
Examples of differential equations that can be discussed are:
- Heston partial differential equation from finance
- Stochastic differential equations for stock prices
- Helmholtz equation for sound waves
- Maxwell equations for electro-magnetic fields
- Schrödinger equation from quantum physics