@Preben Alsholm 

Your observations make sense to me. Here is some info regarding Physics:-Version() that may help to determine what is going on with nm's Maple installation. The output of Physics:-Version() is as follows:

• The MapleCloud version reported is the one reported by PackageTools:-GetProperty(5137472255164416, "X-CloudVersion")
• The library reported, from where Physics is being loaded, is the first library in the list returned by LibraryTools:-FindLibrary('Physics')
• The timestamp is the one returned by LibraryTools:-Timestamp(P)[1]
• The version reported as "installed in your computer" is the one returned by PackageTools:-IsPackageInstalled("Physics Updates", ':-output = :-version')

From what you say, somehow, PackageTools:-IsPackageInstalled("Physics Updates", ':-output = :-version') is telling that version 264 is there. So it found Physics Updates (the whole or portions of it) in the toolbox\2018 directory. I would remove everything below toolsbox\2018, entirely, then check what is being reported. Likewise, if I were to re-install Maple, I would first uninstall Maple, using its unistaller, then remove, manually, all the Maple directory, using the File Manager, then re-install it.

Finally, suppose you have Maple working fine again. If the problem in your computer happens only when you use PackageTools:-Install, I can't imagine what could that be (support@maplesoft.com can) but I can suggest a workaround. In your maple.ini (in mac it is called .mapleinit) you can set the value of libname. Set it as in

libname := "the directory you prefer", libname:
 
Then, libraries (.mla or .maple) found in "the directory you prefer" will be scanned before those found in the (default directories of) libname. All this is explained in ?libname. Then download any package (not using PackageTools:-Install, just downloading them), and place the downloaded .maple file in "the directory you prefer". Then open Maple and everything found in "the directory you prefer" will be loaded from there instead of from the default directories of libname. That is a way to install the package manually, without using PackageTools:-Install. The drawback of this approach is that you need to manually install/uninstall every time, 

BTW another question: what is the value of libname for you? It should contain the toolbox directory.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

You mentioned many things. Let me see if I can help you with this not-understood problem you are having.

• Physics:-Version tells you mainly three things: the directory from where Physics is being loaded (it could be present in many places but it is always loaded only from one place), the version in the MapleCloud and the version installed in your computer.
• Physics comes with Maple, installed within the Maple library (for Maple 2018.2, that is updates.mla).  The "Physics Updates" library, however, is always found in ".../maple/toolbox/2018/Physics Updates", where "..." represents your particular configuration. From what you posted, apparently, "..." is "C:\Users\me"
• There is no relevance in whether you use \ or /, the Maple system handle both path separators in equal footing.
• After you Package:-Install or PackageUninstall something, you always need to restart (in your worksheet and cmaple session, apparently, you didn't restart).
• You can also install the package manually:
  • Open your File Manager, go to C:\Users\me\maple\toolbox\2018, and delete the Physics Updates directory.
  • Go the Maplesoft R&D Physics webpage and download the "Physics Updates" package (apparently, you already have it downloaded)
  • Open cmaple and enter PackageTools:-Install("the full path of the file Physics+Updates.mla"). In my case, that reads PackageTools:-Install("/Users/ecterrab/Downloads/Physics+Updates.maple"); the package installs fine. Or otherwise there is a permission problem (more at the end)
  • Open the worksheet I posted in this thread, Update_v.264.mw, and execute it: the two PDE problems should get solved.

Now, independent of resolving the problem manually, from all the information you gave, I'd imagine there is indeed a problem in your computer regarding permissions, The error in cmaple you show is "permission denied when trying to copy to C:\Users\me\maple\toolbox/2018/Physics Updates/lib/UpdatesPhysics2018.help". I use Macintosh but note that other people using windows (e.g. tomleslie) are not having this permission problem. There is for sure a way to adjust the rights so that you, as an administrator of your computer, can allow Maple to copy a file from one place to another.

Hope this time it fixes the problem ... Best

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

@nm

I already uploaded v.264, then installed it in my copy of Maple, it worked fine. Version 264 has several refinements that make the code find a solution for some more difficult examples. These are two of them:
 

Download Update_v.264.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions.

@Preben Alsholm 

You missed solve's option 'allsolutions' (one could argue it should be used by default, that is another story). With it, you have:

@Preben Alsholm 

I saw this comment by you only today. The distrubuted Maplesoft Physics Updates got updated with the _libraryversion number of Maple 2018.2.1 a week or so ago. Since then, the Warning message you saw is not displayed.

In regards to your comment, there is the "why" and the "what message".

The "why": as you know the Maplesoft Physics Updates pack not just updates to Physics but also to the Differential Equations and Mathematical Functions code, and bug fixes not in those three areas but necessary for them to work properly, some of these mentioned in previous Mapleprimes posts.

Now, Maple is a very interconnected set of software routines. If you use an adjustment in the code written for Maple 2018.2 with a different library, e.g. 2018.1, or the other way around, I cannot assure you that all the things will work as intended. That is the "why" of the message, that includes a sentence (not shown in your comment) that indicates from where you can download an update for the version of Maple you have.

I imagine you know the "why" above but didn't find the message appropriate anyway, So, what message would you find more appropriate for this situation?

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@John Fredsted 

The current Maplesoft Physics Updates will not work well in previous Maple releases. Many of its features depend on things that only exist in Maple 2018, and several fixes only work as expected with the library of Maple 2018. I'd suggest you to install the latest Maplesoft Physics Updates for Maple 2017, but it does not include the change I did yesterday regarding this issue you mentioned.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@lucenalex 

I'm a bit overloaded today and tomorrow but will try to find time to show how to formulate the problem - hopefully before a couple of days from today.

Best

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Sofi 

The Maplesoft Physics Updates with code for solving the PDE & BC you posted only works for Maple 2018. Regarding the math (your other question), give a look at  this other Mapleprimes post where it is all explained.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Mariusz Iwaniuk 

Note that the solution you posted, using new routines described in this other Mapleprimes post, actually shows two equations for lambda[n], one of which is sort of redundant (due to an intermediate call to simplify that split the single equation into two). This is adjusted in version 200 or higher of the Maplesoft Physics Updates, so that now the output has one single equation defining lambda[n].

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Rouben Rostamian

 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Download The_other_two_issues.mw

@Mariusz Iwaniuk 

Thanks, version 194 includes also a fix to factor, but the advanced version of that fix got by accident into the code for 2018.2. It is corrected now in version 195 of the Maplesoft Physics Updates.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Rouben Rostamian  

First of all, nice reply yours. It is exciting when the level of the discussion goes higher and at the same time stays respectful of other's (sometimes different) opinions.

On the contents: you are right in the distinction about classical and weak solutions; mainly: the solution could be discontinuous at the boundary conditions (e.g. in the example posted). So yes, I goofed here, prematurely discarding the problem because of the inconsistency of the boundary conditions posted.

On the other issues that resulted from this post: Maple's pdsolve does compute weak solutions, examples of that were posted, but the one of this post is not solved when it could - for instance, you show how - and the method (skipping details) is systematic. To cover this example and a family of related cases more work is necessary. We are working on that in this moment, among other things. I will post here again when it is ready.

@Carl Love 

Physics:-Fundiff implements functional differentiation, it computes a functional derivative, an operation at the realm of variational calculus. Because Physics is all about a principle of minimal action - a variational principle - it so happens that basically all formulations in classical and quantum physics require computing functional derivatives (of the action, and equating the result to 0). If one day you happen to work with variational calculus you will be surprised with the computational power behind Fundiff . Some of it is shown in several posts here in Mapleprimes about quantum mechanics and classical field theories.

If you are still not finding the computation familiar, check Wikipedia at https://en.wikipedia.org/wiki/Functional_derivative - to go to the point, search the page for Functional derivative o a function.

On the other hand, Physics:-diff implements, in a general/formal sense what in jet calculus is called jet space - frequently mentioned in the context of differential equations. Generally speaking, you consider independent variables, dependent variables, and their partial derivatives as a set of equivalent independent objects with respect to which you can differentiate. For example, all the Lie theory of symmetries of differential equations is based on this concept (to see the simplistic core of the implementation, give a look at ?PDEtools:-ToJet). The implementation of Physics:-diff in computer algebra is tricky due to the way Maple's diff (without Physics) got implemented day one, making necessary to implement together the concept of "computing the derivative with respect to x at fixed f(x, ...)" (see the help page), and in this way implement, for the first time in Maple, true partial derivatives, for real, as the ones you use when formulating thermodynamics for instance.

People sometimes think of these two commands as interrelated because, if you are functionally differentiating an integral, you can frequently express the result using a sum of terms all of which involve calls to Physics:-diff. But these two commands are actually different. Most of the things mentioned above are described in more details in the corresponding help pages.

By the way, it is remarkable that while these commands are at the very core of formulations in Physics, I actually coded them using Maple in 1994, they where my first programs, and it was the first time these operations got implemented in computer algebra - I even published a paper with them in Computer Physics Communications, still today there is no equivalent for them in Mathematica.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

There is clearly an issue here (BTW, good catch vv!), as usual splitting into two: "what is happening?" and "is that ok?". What is happening: Change is a wrapper for PDEtools:-dchange; debugging it you see that its input for 2J is not nearly the same as for J - mainly in the case of 2J only, the change of variables is performed first in the inner integral. The undesired output for J (not for 2J) appears while changing variables in J taking the iterated double integral as a multiple integral. "Is that OK?": generally speaking yes, however in cases like this changing variables one integral at a time takes you to a much simpler and readable result.

I'll give this a closer look later today or tomorrow and adjust the code to return the simpler form - then upload the adjustment within the next "Maplesoft Physics Updates for 2018.1" - will write here when it's ready.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Carl, very beautiful post, illustrative and insightful!

Best

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft