# Dagothar's Den

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The wave equation

The famous second order linear partial differential equation, known as the wave equation, describes the behaviour of all sorts of waves, including acoustic and electromagnetical:

${ \partial^2 u \over \partial t^2 } = c^2 \nabla^2 u$

The visualization was an exercise in solving differential equations numerically. It shows the interaction of waves generated from two point-like sources.

This equation is tiny, elegant, yet powerful: its simple form hides both the wondrous phenomena of resounding strings of an instrument, and the play of light on the surface of a pond.

(I didn’t know how to make the waves not to reflect at the edges of grid. But then I figured out: a shore. Waves are dissipated as the sea floor raises gently - the damping is progressively higher on the edges. Is there a better way to simulate an infinite grid?)

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