Using MaxStepFraction as ticks on plot

Question

Is there any way I could use the MaxStepFraction (or grid size) as used in NDSolve in the example below as ticks on the 3d Plot?

That was I would be able to plot the grid points on the X and Y axis.

I tried creating a table and using that as the argument in Ticks but that didn't work.

Minimum working example:

Clear[u, L, t, x, y, sol, Eq]
L = 4;
Eq = -D[u[t, x, y], t, t] + D[u[t, x, y], x, x] + 
   D[u[t, x, y], y, y] + Sin[u[t, x, y]];
uSol = u /. NDSolve[{
     Eq == 0, u[t, -L, y] == u[t, L, y], 
     u[t, x, -L] == u[t, x, L], 
     u[0, x, y] == Exp[-(x^2 + y^2)], 
     Derivative[1, 0, 0][u][0, x, y] == 0
     }, 
    u,
     {t, 0, L/2}, {x, -L, L}, {y, -L, L},
    MaxStepFraction -> 1/11
    ][[1]]




tt = 1.2;
Plot3D[ uSol[tt, x, y], {x, 0, L}, {y, 0, L}, 
 Ticks -> {{0, 2/5, 4/5, 6/5, 8/5, 2, 12/5, 14/5, 16/5, 18/5, 4}, {0, 
    2/5, 4/5, 6/5, 8/5, 2, 12/5, 14/5, 16/5, 18/5, 4}}]

The ticks in the above figure were created using, Table[i 4/10, {i, 10}] and then manually pasted into the curly brackets. Obviously, that isn't the most efficient way.

I tried pasting the Table command inside Plot3D but that didn't work.

Answer 1

tt = 1.2;
Plot3D[uSol[tt, x, y], {x, 0, L}, {y, 0, L}, 
      Ticks -> {Table[i 4/10, {i, 10}], Table[i 4/10, {i, 10}]}
]

or the slightly more concise version of mr.wizard:

Plot3D[uSol[tt, x, y], {x, 0, L}, {y, 0, L}, 
  Ticks -> ({#, #} & @ Table[i 4/10, {i, 10}])
]

yield:

or, since you wanted to use your setting for MaxStepFraction (1/11), you could use FindDivisions with that value:

tt = 1.2;
Plot3D[uSol[tt, x, y], {x, 0, L}, {y, 0, L},
      Ticks -> {FindDivisions[{0, L, 1/11}, 10],FindDivisions[{0, L, 1/11}, 10]}
]