In a final project for a sophomore mathematics class, my partner and I worked with partial differential equations in MatLab. We developed a web of nodes that could be animated to simulate the motion of a drop of water in a basin. These notes were approximations of derivatives, using linear combinations of values, at different discretized steps. We developed boundary questions for 1-D and 2-D waves. Our first iteration was a 1-D wave animation. Then we developed a 2-dimensional set of equations and created the "pool of water" simulations. We also explored the concept of wave instability, when stability is greater than 1. We assumed that the waves were in their space, unaffected by outside interference.
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