Hello I am trying to use an explicit Euler method and to show the solution is always unstable no matter the time step.

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๐œ•๐‘‡/๐œ•๐‘ก + ๐‘Ž ๐œ•๐‘‡/๐œ•๐‘ฅ = 0 for 0 <= x <= 1
With the initial condition and boundary conditions of,
๐‘‡(๐‘ฅ, 0) = ๐‘’ โˆ’200(๐‘ฅโˆ’0.25) 2 , ๐‘‡(0,๐‘ก) = 0, ๐‘‡(1,๐‘ก): outflow condition
๐‘Ž = 1, โˆ†๐‘ฅ = 0.01

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