Physics 212, 2018: Lecture 24

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The heat diffusion equation -- one of many partial differential equations (differential equations involving partial derivatives).

• Fick's first law of diffusion ${\displaystyle J=-D{\frac {d\phi }{dx}}}$ or ${\displaystyle {\vec {J}}=-D\nabla \phi }$ (also known as Newton's law of cooling if ${\displaystyle \phi =T}$, or the Fourier law of heat conduction)
• Fick's second law of diffusion ${\displaystyle \partial _{t}\phi =-D\nabla ^{2}\phi }$.
• Finite difference form of the heat diffusion equation; need boundary conditions to complete the solution
• Boundary conditions (implemented with extending the grid matrix):
• Absorbing
• Reflecting
• Peeriodic
• Solution of the equation using Python code.