@Alejandro Jakubi 

Can distributed grid mode computations be done within a single machine by means of the Grid package alone, without the Grid Computing Toolbox?

Yes. I have done it and achieved 100% processor utilization (as reported by Windows Task Manager) over 8 nodes. What would be the purpose of having the Grid package if this were not possible?

@Kitonum In the Question, f is a function of two arguments. That does not correspond with the f in your code.

@TomM This problem is computer-specific. On the majority of computers the space curves show up without needing the linestyle explicitly stated. That's why proofreaders didn't catch it.

Are you interested in analytic solution or numeric solution?

@Carl Love What happened? Did you fix the problem? Please attach the worksheet as explained above.

@mehdi jafari The default values used for spacestep and timestep are not very carefully chosen by pdsolve. They both default to 1/20th of the spatial range. In this problem, that means the timestep is 5, which is clearly too large considering that we are getting 5 plots all with t  < < 5.

@Hummingbird Please attach your worksheet (rather than cut-and-paste) using the green up arrow, which is the last icon on the second row of the toolbar in the MaplePrimes editor.

@mehdi jafari Mehdi, the range is already set by the boundary conditions to -50..50. The range option is only needed when the boundary conditions do not give both endpoints of the space range.

@Hummingbird

In order for

solve({seq(eq[i], i= 1..6)}, convert(phi4N, set));

to work, the eq[i] must be those that you created in the for loop, not those that you entered manually.

The code

solve({seq(eq[i], i= 1..6)}, convert(phi46N, set));

is wrong because the second argument only uses one of the six variables. If you want to solve for fewer variables than there are equations, use eliminate instead of solve.

@Kitonum Clearly the OP did not actually use that .. syntax. There would have been an error message if it had been input like that.

Please show explicitly the code that does not work.

@sarra Remove the range option! That was not in your code when I made my recommendation. Your range is already set at -50..50 by your boundary conditions. Please don't change your original code and then say that my fix doesn't work!

@mahmood180 Please post this as a seperate Question. It seems unrelated to the original.

@c4meleon Change the dsolve command to

res:=dsolve({diff(y(x),x)=f(x,y(x)),y(0)=1}, {y(x)});

You must be using a significantly older version of Maple. Which is it?

@c4meleon Please show your dsolve command that is not working.