pdsolve([PDE1, PDE2], [w1(x, t), w2(x, t)]) generates some output, but I'm not sure if it's what you're looking for; you may need to give Maple more specific input (maybe some ICs).

The message says the independent variable in the equations does not match the 'continuoustimevar' (t) specified by the DynamicSystems[SystemOptions], so double-check the terms in your equation and make sure that you used the same independant variable as what your command is expecting you to use.  If you need further assistance, please post your worksheet.

I assume that method = bvp[middefer] is used to address the singularity that Maple finds when no method is specified, so the error message Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging suggests that the problem was either set up incorrectly to begin with, or it cannot be solved (at least not with this method/approach).

A couple of suggestions:

1. In the first DE, there is a fourth derivative for f(eta), but the ICs only go up to the second derivative. Try adding an IC for the third derivative; the first derivative has two (which may explain the singularity), so perhaps one of them was supposed to be for the third.
2. Since the first two DEs do not use phi(eta), you may want to concentrate on those first, then use the solution for f(eta) to find phi(eta) in a separate call to dsolve().

In general, this error message occurs when either the worksheet or the Maple installation itself has been corrupted, or when Maple senses that some loop will not terminate, some computation would be too demanding (for example 2^(2^32-1)), or Maple was consuming too much of the RAM or CPU during a calculation.

Considering that the code works elsewhere, the worksheet itself is not likely the issue (unless you copied the code rather than transfering the file).  So, if other code works fine on that installation of Maple, the 100x100 Matrix is likely too demanding for the machine you experienced the issue on. This could be a hardware limitation, but you might also have been using 32-bit Maple (which has limited memory).

Hi Lilian,The source of the issue for list_1 appears to be rooted in the feasibilitytolerance option.  Without any constraints, there is no need for the option (only optimalitytolerance would be relevant), so when Maple executes the call to LSSolve, Maple's algorithms seem to find the minimum without any issue.  However, by adding constraints at zero, Maple's algorithms seem to change, now looking at values even closer to 0 and (for some reason) ignoring the ones further away.

As you may have guessed by the mention of the feasibilitytoleranceoption, Maple's algorithms are designed to violate constraints in order to achieve a better solution.  However, they will only do so if the violations are within the set feasibility tolerance. The LSSolve help page does not seem to specify what the default feasibility tolerance actually is, but you will notice that the negative value that you saw was a very small number (i.e. reasonably close zero).  If you incorporate a suitably small tolerance, the negatives go away (see attached).

Admittedly, this still doesn't quite explain why the new minimum is actually larger.  However, considering that, as you pointed out, the constraints were redundant to begin with, the notion of feasibility tolerance makes those constraints inadvisable anyway.

For list_2, the initial call to LSSolve did yeild a negative value, so incorporating a constraint to avoid it is perfectly reasonable.  However, based on what we now know about Maple's feasibility tolerance in problems like these, only one constraint should be used.  Once it is added, another negative does come up, but after a constraint is added for that one, no others appear (see attached).

On a side note, you may want to consider upgrading to 2016.2.

Download worksheet_help_-_TS.mw

For most custom-made packages, the relevant files need to be saved in/extracted to

C:\Program Files\Maple 2016\lib

on Windows or

//Library/Frameworks/Maple.framework/Versions/2016/lib

on Macintosh.  If you are not familiar with using these directories (which can interfere with your installation of Maple if modified incorrectly), you can also install an add-on package to a specified user library folder:

If you have previously added a custom user library path to 'libname', please copy the library file “%PackageName%.mla” to that folder. If you have not, you may add that user library folder by doing the following:

1. Copy “%PackageName%.mla”  to a user library folder. If you do not have a user library folder, simply create a folder for your Maple library files. This folder may be located anywhere on your computer, though a suggested path is to create a new folder called MapleLib in your "home directory" and place the files there. To find your home directory in Maple, use kernelopts( homedir ) ; For more information, see the kernopts help page.
    
2. Open your Maple initialization file. See the initialization file help page for details on how to create and configure these initialization files.
    
3. Add the line: libname := libname, "PathToUserLibraryFolder” : For example, to add the path to your "MapleLib" folder under your home directory use libname := libname, cat( kernelopts( homedir ), kernelopts( dirsep ), "MapleLib" ) :
    
4. Save your Maple initialization file and restart Maple.

From there, you should be able to load the package using the with() command.  For more information, see the with command help page.

It looks like those particular values of m, N, and h are outside of the range that Maple can currently handle for this problem; the closest set of values I can get an answer for is m=2, N=17, h=0.41600. 

In most cases, even using N=16 results in an echoed call to fsolve(), so it might be difficult to find a way to get these values any closer to what you're hoping for, but hopefully this set gives you a good starting point. You may also want to consider trying to rewrite the equations in an different form.

You're right, this is an issue that our developers hope to have resolved for 2017.2.  In the meantime, please try launching Matlab via the 'matlab' script rather than the app bundle.

Thanks for the post.  Can you send us a copy of this worksheet?  Please also try some simple computations (such as 1+1), and test cmaple.  -support@maplesoft.com