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Joining InterpolatingFunctions into Piecewise - doman?


I would like to solve a diff eq on a very large interval, therefore I
solve it on successive intervals.
When putting the results together I get a _relatively_ good figure and
an error message.
Note that there is a hole on the graph of the function. Any other
solution to join InterpolatingFunction objects would be appreciated.

Thank you, Janos

f[ini_, tlast_] :=
 Module[{from = tlast, to = tlast + 1,
   X}, {X = (x /.
       NDSolve[{x'[t] == -0.5 x[t], ini}, x, {t, from, to }])[[1]],
   to, X[to]}]
nl = NestList[f[x[#[[2]]] == #[[3]], #[[2]]] &, {zzz, 0, 2.0}, 3];
full[t_] :=
 Piecewise[
  Transpose[{Table[nl[[k, 1]][t], {k, 2, 4}],
    Table[k <= t < k + 1, {k, 0, 2}]}]]
Plot[full[t], {t, 0, 3}]


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