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Wed 19 Apr 2023 21:57:13
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Clear["Global`*"];d=50;numSteps=30;discretize[expr_]:=N@Table[expr/.{ii0},{i0,0,d-1}];ones=discretize[1];ii=DiagonalMatrix[ones];steps=Range[0,numSteps];ann[vals_]:={steps,vals};p=0.5//N;e0=1;h=/z;{e0$,h$}=discretize/@{e0,h};h$=h$/Total[h$];A=2DiagonalMatrix[h$]-{h$}.{h$};eigs=Eigenvalues[A];ListLogLogPlot[{eigs,Diagonal[A],2h$},Joined{True,False,False},PlotLegends{"2h","eigenvalues"}]
-p
(i+1)
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Max@Abs[eigs-Diagonal[A]]
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0.0051149
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Max@Abs[eigs-(2h$)]
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0.00523789