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Feb 27, 2019 at 17:47 comment added Antoine Conze To get some insight, rewrite your equation as $U^{n+1}_j = \frac{k}{h^2}U^n_{j+1}+ (1-2\frac{k}{h^2})U^n_{j} + \frac{k}{h^2}U^n_{j-1}$. The weights $(\frac{k}{h^2}, 1-2\frac{k}{h^2}, \frac{k}{h^2})$ can only be interpreted as a Markov chain transition probabilities iff $k \leq h^2/2$.
Feb 26, 2019 at 16:46 comment added FunnyBuzer please have a look at the links in my answer. If you are satisfied, please mark the answer as the solution.
Feb 26, 2019 at 15:29 answer added FunnyBuzer timeline score: 3
Feb 26, 2019 at 14:53 history asked Victor CC BY-SA 4.0