See if the attached worksheet makes things any clearer

plotProb.mw

which is not zero - oh yeah, says who exactly?

Because none of your bcs or pde are capable of making this assertion.

All of your equations are perfectly satisfied with w(x,y)=0, why aren't you.

Please explain: or perhaps supply some equations which are not satisfied with w(x,y)=0

fsolve() provides "the numerical solution of the same problem" - that's what fsolve() does!

What makes you think that the answers provided by fsolve() are incorrect???!!!

so I'm going to make it easy for you. You have the boundary conditions

bc1 := w(0,y) = 0; # @ x=0 edge;
bc2 := w(a,y) = 0;  # @ x=a edge;
bc3 := w(x,0) = 0; # @ y=0 edge;
bc4 := w(x,b) = 0; # @ y=b edge;
bcx1 := -D11*D[2](w)(0,y) - D12*D[2](w)(0,y) = 0; # @ x=0 edge;
bcx2 := -D11*D[2](w)(a,y) - D12*D[2](w)(a,y) = 0; # @ x=a edge;
bcy1 := -D12*D[2](w)(x,0) - D22*D[2](w)(x,0) = 0; # @ y=0 edge;
bcy2 := -D12*D[2](w)(x,b) - D22*D[2](w)(x,b) = 0; # @ y=b edge;

Please specify which of these is not met by the solution w(x,y)=0. All you have to do is just pick one of bc1, bc2, bc3, bc4, bcx1, bcx2, bcy1,bcy2 - and state clearly why w(x,y)=0 does not satisfy the condition - so which of the above is not satisfied by w(x,y)=0?

Similarly, in the equation

myPDE1 := D11*diff(w(x,y), x$4) + 2*(D12+2*D66)*diff(w(x,y), y$4) + D22*diff(w(x,y), x$2, y$2) - G*diff(w(x,y), x,y)= 0;

you have to explain clearly why this is not satisfied by w(x,y)=0, because I can assure that you will get,

myPDE1 := D11*0 + 2*(D12+2*D66)*0+ D22*0 - G*0= 0;

Are you suggesting that this is not true???

Just because you don't "like" the answer, doesn't make the answer wrong

alpha[1] and alpha[2] don't exist in the worksheet you supplied - hence cannot be solved for.

CAn't help with Maple17 issue, I only have Maple18, Maple2015 and Maple2016 loaded

In order for the 'implied multiplication' feature to work correctly when using 2D input, you need a space between 'a' and 'x' in the term '2ax' or enter the multiplication sign explicitly - or use 1-D input which makes typos like this easier to spot

If I run your code using Maple 2016.1

SOL := {alpha = 18.52560490773176, beta = 22.87185195383078, delta = 23.53749276266458, theta = -47.69221692042093, upsilon = -.7905750709173283, xi = 9.460741609314995}

with no warnings or errors.

I said that I suspected that the solution of f(y,t) might be complex for all beta>0

This was based on examining the general (ie analytic) solution for the PDE, which contains mulitple terms involving sqrt(-2.0*beta). See the attached

pdeProb.mw

Please post code using the big green up-arrow in the Mapleprimes toolbar, otherwise I'm guessing?

For example, you state

V[i] := vector[row]([h, r, delta])        { h,r are variables of loop; delta is a root}

so what determines the value of 'i' in V[i].

Why are you using the deprecated 'vector()' command, rather than 'Vector()' - do you have a really old version of Maple?

How was the array V initialised? Did you use 'Array()' or the deprecated 'array()'

Kitonum's code is correct.

Use the big green up-arrow in the Mapleprimes editor to post the code of the failing worksheet,  cos otherwise we're just guessing

the required solution f(y,t) is a complex-valued function. Now I could be wrong but I don't think that pdsolve/numeric handles complex-valued functions.

It may be possible to get round this by defining two new functions as the real and imaginary parts of f(y.t) and solving the resultant system of two pdes - but before I investigate this any further, I'd like confirmation that f(y,t) is indeed comple-valued. So far as I can tell, this will always happen if beta>0.

You state that you have an analytic solution - is it complex-valued?

Post this solution, it might help.

Nothing wrong with Kitonum's answer, but if you are actually generating the data using a couple of for/while loops, you might want to consider using something like

Matrix( NumberOfRows, NumberOfColumns, (i,j) -> f(i,j) )

where 'i' is the row index, 'j' is the column index and f(i,j) is a function which generates appropriate values. This might remove the need for the 'while' loops which generate your arrays.

A possible drawback with this approach is that you have to be able to specify the (i, j)-th entry explicitly in terms of the index variables 'i' and 'j'. If the (i, j)-th entry depends on the (for example) (i-1, j-1)-th entry, then this approach is not possible (so far as I am aware!)

If you have a question - just ask it. We do the best we can

Sometimes posters ask a question, which can be/is answered, but generates another thought.

For example, in your case, the way your question is posed, we have to start from a 'single database' which has to be split for subsequent parallel processing. So a fairly obvious thought arises - if one generated the original data in some "parallel" process, could one do better???

Note that this is not any kind of criticism - it is just an observation of the fact that if you are going to go 'parallel' in a calculation, what is the best point to go 'parallel'. Answer is (probably) as early as possible!

So, have I provided you with best answer possible? - well maybe/maybeNot

Just because you (as a user) have administrative privileges does not mean that an application (such as Maple) assumes administrator privileges. After all this would give Maple free rein to overwrite everything on your 'C' drive - including the operating system. I assume that you don't want that to happen. So Maple can be a little "conservative" about what/where it can read and write

Two possible solutions

1. Recommended solution: Store Maple files in a place where a well-behaved piece of software might expect to have access without administrator privileges - probably something like "C:/Users/yourUserName/Roaming/Maple/possiblyMapleVersion/fileName". Pretty sure that (by default) Maple will have read/write acces to such a location - and all error/warning messages will disappear
2. Not Recommended solution. Run Maple as Administrator - precise method depends on how you normally invoke Maple. If from a desktop icon, then right-click and select 'Run as Administrator'. Starting from anywhere else - eg Start Menu or executable in a file browser - you still need to right-click the .exe and 'Run as Admistrator'. Note that I do not recommend any of these, cos you really really do not want to give an application 'Administrator Rights'. It may not be very likely, bt it has the potential to do serious damage to your OS installation!!!!

You have 9 equations, in 27 unknowns, for which you request the solution for 46 quantities

The basic theory of simultaneous equations tells you that if you have 9 equations then you can explicitly solve for 9 (or fewer) unknowns - so I have no idea what you are actually trying to achieve in this process!

The attached worksheet (which runs without warnings or errors) gives you the best "solution" you are going to get - and it is pretty much entirely meaningless - because your original question is pretty much meaningless

solSimEq.mw