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I am using the FTCS method for solving differential equations. I know that the condition for stable output is $$ \frac{\alpha \Delta t}{\Delta x ^2} < \frac{1}{2} $$ But when I use the distance step according to this formula, the size of the step is big and the answer I get is wrong. Is there some way I can use smaller distance steps in FTCS?

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  • $\begingroup$ I suppose that you are solving the heat equation in 1D, is that right? $\endgroup$
    – nicoguaro
    Jul 2 at 17:01
  • $\begingroup$ The condition only says that the time step can't be too large, but is there a corresponding condition that you can't choose it very small? $\endgroup$ Jul 4 at 1:04
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The are some who would say that this is the price you pay for not having to invert a matrix. You traded relatively cheap timestep updates for accuracy. You could switch to an implicit method and take as fine a grid as you like at the cost of having to solve a linear system at each timestep.

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