@Christopher2222

This code was copied from a post that I made to either comp.soft-sys.math.maple or sci.math.symbolic over a decade ago. At that time, gcfreq= 2^22 was large enough to effectively stop garbage collection during the course of the timing. On today's computers, that value is absurdly small. The usage of gcfreq has been deprecated.

Also, why compare time[real]? I think time(...) (processor time) would be a fairer comparison.

Making those changes, I get

M16/64 on Win 7.1 Intel i5x4 @ 3.2 GHz: 0.374 sec.

I prefer the StackExchange way. But note that there is an option on MaplePrimes to sort chronologically. It would be great if MaplePrimes were a StackExchange site, but they require a core of 200 dedicated users to start a site.

@Andriy Even shorter is

f:= `+`:

But I think that the OP wanted to ask the question about _params and was just using addition as a trivial example. I think that the OP had in mind a more sophisticated use of _params.

@Joe Riel I disagree. The relationship between $ and seq is essentially the same as that between sum and add. The $ allows for the entry and manipulation of indefinite sequences, such as

k:= 'k':  n:= 'n':
k^2 $ k= 1..n;

The backslash in \%1 is superfluous. The command might as well be

error "bad argument: %1", n

Don't expect to see the backslash in any help that you find on the error command.

@Alejandro Jakubi I've only used Grid:-Map.

@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.