The Diffusion Equation Solved Analytically With Python
Today, we will use Python to analytically solve one of the most important partial differential equations out there, the diffusion equation. It is a fundamental equation that arises in many areas of physics, chemistry, biology, and engineering, and has an enormous range of applications. For instance, in physics, the diffusion equation is used to describe the movement of heat through a solid or fluid, as well as the transport of particles in gases and liquids. Also, the Schrödinger equation is (in principle) a kind of diffusion equation. In biology, the diffusion equation is used to study the movement of nutrients and other substances through living tissues, as well as the spread of diseases. In engineering, the diffusion equation is used to design and optimize processes such as heat exchangers, catalytic converters, and solar cells. It is even applied in economics, where the diffusion equation can be used to model the spread of ideas or innovations through a population. Due to its wide range of applications, it is not surprising that it was found independently by several scientists of the 19th century working on completely different topics. The famous George Gabriel Stokes derived the equation in 1845 to describe the motion of fluids, while the even more famous James Clerk Maxwell derived the…
