I have solved two coupled equations with `{Solf, Solg} = NDSolveValue[eqns, {f, g}, {x, 0, L}, {t, 0, tmax}]`

and want to extract the computational grid `{x,t}`

with `InterpolatingFunctionDomain`

and `InterpolatingFunctionGrid`

to observe the spatial mesh and to plot the time steps. In addition, sometimes it cannot compute a solution over the full time-interval that I specified, so I want to plot the solution that was computed in order to understand what might have gone wrong.

By reading the document, I know how to do this when using `NDSolve`

to solve a single equation for `h[x,t]`

. For example,

`hSol = First[h/.NDSolve[eqn, f, {x, 0, L}, {t, 0, tmax}]] hGrid = InterpolatingFunctionGrid[hSol] Dimensions[hGrid] (*determine mesh points in each dimension*) {Tini, Tfinal} = InterpolatingFunctionDomain[hSol][[2]] (*extract the time interval*) tList = hGrid[[mesh-position, All, 2]]; (*here the 'mesh-position' can be chosen according to the output of Dimensions[hGrid]*) `

Then we can plot the time steps at the mesh-position using

`ListLogPlot[tList, PlotRange -> All, Frame -> True, FrameLabel -> {"step", "t"}] `

**But I cannot extend these to the case in which I used **`NDSolveValue`

to solve two coupled equations for `f[x,t]`

and `g[x,t]`

, as mentioned above. For example, using `hGrid = InterpolatingFunctionGrid[Solf]`

and `Dimensions[hGrid]`

I obtained `{1}`

, which was clearly wrong and should be in the form of `{number-of-space-mesh, number-of-time-step, 2}`

.

I think the problem results form the structure of the output of `{Solf, Solg} = NDSolveValue[...]`

. In this case the output is in this form: `{InterpolatingFunction[{{0.,L},{0.,tmax}},<>],InterpolatingFunction[{{0.,L},{0.,tmax}},<>]}`

. Please help.

Here is an example from the document of `NDSolveValue`

:

`pde={\!\( \*SubscriptBox[\(\[PartialD]\), \(t\)]\(u[t, x]\)\)==\!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]\((\((v[t, x] - 1)\)\ \*SubscriptBox[\(\[PartialD]\), \(x\)]u[t, x])\)\)+(16 x t-2 t-16 (v[t,x]-1)) (u[t,x]-1)+10 x E^(-4 x),\!\( \*SubscriptBox[\(\[PartialD]\), \(t\)]\(v[t, x]\)\)==\!\( \*SubscriptBox[\(\[PartialD]\), \({x, 2}\)]\(v[t, x]\)\)+\!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]\(u[t, x]\)\)+4 u[t,x]-4+x^2-2 t-10 t E^(-4 x)}; bc={u[0,x]==1,v[0,x]==1,u[t,0]==1,v[t,0]==1,3 u[t,1]+(u^(0,1))[t,1]==3,5 (v^(0,1))[t,1]==E^4 (u[t,1]-1)}; {usol, vsol} = NDSolveValue[{pde, bc}, {u, v}, {x, 0, 1}, {t, 0, 2}] `