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Instability in wave equation

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When I make use of Smith's numerical solution to the wave equation, the calculated curve become instable after some time intervals. anybody know why and how to solve this problem? thanks
 
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Dear STUYY
IN such analysis time step is a main element regarding stability. of course the explicit and implicit methods differ in that regards. Please use shorter time steps and if the problem stays on change the method to an implicit one.
 
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