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Your idea of taking matrix powers is not a good one. You should code it for step by step updating $$ u_0 = \textrm{initial condition} $$ $$ u_0 \rightarrow u_1 \rightarrow u_2 \rightarrow $$ so at any time you at most store two levels of solution $u_n, u_{n+1}$. Even when updating $u_n \rightarrow u_{n+1}$ I would avoid using a matrix since you are ...

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