I'll start with the one which I call the discrete heat problem: Consider the points (i,0)(i∈Z;0≤i<n;2≤n). Each has an amount of heat, which we'll denote Ei(t) as a function of time. Suppose we are given Ei(0)(0≤i<n). Can we find explicit expressions for Ei(t)?
The problem can be solved one part at a time, each part being interesting on its own, so I have decided to split the problem into several posts. Here's an outline of my solution:
- Create a differential equation
- Solve the characteristic equation
- Create an associated linear equation (almost done!)
- Solve the linear equation (not done yet!)
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