1. Numerical Modelling

The Finite Difference Method (FDM) is a fundamental numerical approach used to solve differential equations that govern physical phenomena. These phenomena include heat flow through media, the distribution of stresses in solid structures, fluid flow through porous media, pollutant dispersion in the air and water, amongst others. Virtually, any physical phenomena can be tackled by solving numerically differential equations. The FDM provides engineers with the flexibility to model and analyze a complex geometries with varied past, present and future scenarios, optimize designs, ensure safety, reduce costs, and predict failures. Even more!

In this Chapter, the fundamentals of numerical modelling and basic numerical methods are treated. More advanced techniques are also revised. The main focus is on Ordinary Differential Equations of varying orders.

Fig. 1.1 Cool numerical model of the Yamuna river. Thanks to Amgad Omer (Deltares).