# Coordinates of MeshPoints

The output of a set of differential equations solved with NDSolve produces a series of curves and I need to obtain the spacing between these curves at a given level on the y axis. I use MeshFunctions and Mesh to produce points on the plot. I need to find out the {t,y} values of these points.

The nb is as follows:

eqns = {Table[y[i]'[t] == 15 - (Exp[i]*10*Exp[-2*t] + 3)*y[i][t], {i, 0, 3}],
Table[y[i] == 5, {i, 0, 3}]};
sol = NDSolve[eqns, Table[y[i], {i, 0, 3}], {t, 10}];

Plot[Evaluate[Table[y[i][t], {i, 0, 3}] /. sol], {t, 0, 6},
MeshFunctions -> {#2 - 3 &}, Mesh -> {{0}}];

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If you want the two solutions for each i:

r = {};
eqns = {Table[y[i]'[t] == 15 - (Exp[i]*10*Exp[-2*t] + 3)*y[i][t], {i, 0, 3}],
Table[With[{ii = i}, {y[i] == 5,
WhenEvent[y[ii][t] == 3, AppendTo[r, {ii, t}]]}],
{i, 0, 3}]};
sol = NDSolve[eqns, Table[y[i], {i, 0, 3}], {t, 10}];
r

(*
{{0, 0.0605192},  {0, 1.00734},
{1, 0.019865},   {1, 1.5086},
{2, 0.00705075}, {2, 2.0086},
{3, 0.00256151}, {3, 2.5086}}
*)

LogLogPlot[
Evaluate[Table[y[i][t], {i, 0, 3}] /. sol], {t, 0.000001, 6},
MeshFunctions -> {#2 - 3 &}, Mesh -> {{0}}] • Thank you, it worked. Idially, I would prefer only the points after the minimae. (i took latin a large number of years ago.) – Jean-Pierre Raynauld Mar 31 '15 at 22:12
Flatten[Table[NSolve[(y[i][t] /. sol) == 3, t], {i, 0, 3}], 2]


(* {t -> 1.00734, t -> 1.5086, t -> 2.0086, t -> 668.12} *)

• Three first points are OK but last one is wrong (668,12). – Jean-Pierre Raynauld Mar 31 '15 at 22:19
• @DavidG.Stork Sure? Try eqns = {Table[ y[i]'[t] == 15 - (Exp[i]*10*Exp[-2*t] + 3)*y[i][t], {i, 0, 3}], Table[y[i] == 5, {i, 0, 3}]};sol = NDSolve[eqns, Table[y[i], {i, 0, 3}], {t, 0, 700}];Plot[Evaluate[Table[y[i][t], {i, 0, 3}] /. sol], {t, 0, 700}, PlotRange -> {0, 6}] – Dr. belisarius Mar 31 '15 at 23:53
• Ah.. the solution from the range {0, 10} in the problem does not extrapolate accurately to large $t$. Indeed if you force the solution range to be large, you get a (slightly) different solution. Fair enough. – David G. Stork Apr 1 '15 at 0:15