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{{PHYS212-2018}}

The heat diffusion equation -- one of many partial differential equations (differential equations involving partial derivatives).
*Fick's first law of diffusion <math>J=-D\frac{d\phi}{dx}</math> or <math>\vec{J}=-D\nabla \phi</math> (also known as Newton's law of cooling if <math>\phi=T</math>, or the Fourier law of heat conduction)
*Fick's second law of diffusion <math>\partial_t \phi = -D\nabla^2 \phi</math>.
*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.

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Physics 212, 2018: Lecture 24 - Revision history

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