@acer That's a good catch!  I should have thought of that.  Thanks for pointing it out.

@fkohlhepp What you have posted is still incomplete since the data file NACA0012 CDalpha.csv is missing.

But all those details should be unnecessary.  Try entering

eqn2(theta);

If MapleFlow works like Maple, that should print out the equation in all its glory.  Just copy and paste that single equation.  Nothing else is needed.

@fkohlhepp As Axel Vogt has suggested, it would be best if you could just post your eqn2 in a plain text Maple notation.  The details of how that equation is arrived at would be immaterial.  Then people can copy and paste that equation into Maple and suggest good ways to solve it.

In the absence of that equation, I have made up something which is remotely similar.  Maple's fsolve() indeed has difficulty solving the equation—I don't know why—but the NewtIt() proc which I posted earlier solves the equation right away.

Download tryme.mw

@fkohlhepp Regarding "its already essentially here in another post": That's not good enough. Your problem lies in the definition of the function Thust which you have not shown. The more information you provide, the better help you will get, and perhaps it may turn out that your "home-built" iteration scheme is not needed at all.

@Mohamed Mohsin If you don't know how to solve a problem, try to find an easier problem that you can solve.  If you don't know how to solve that easier problem, find even an easier one, and so on, until you arrive at a point where you are able to do something.

For instance, in your case, do you know how to solve

D^γ S(t) = S(t)

and if not, do you know how to solve

D S(t) = S(t)

and so on.

You should also ask yourself:

• Do I know anything about fractional differential equations?
• Do I know anything about the homotopy perturbation method?  

Answers to these questions have nothing to do with Maple. Begin with investigating these mathematical prerequisites of your master's thesis.  Coding and calculating with Maple will come only after you have positively answered those questions.

I assume that you have done more for your master's thesis than what you have shown here.  Explain what you have so far, and where it is that you need help with Maple.

Otherwise it looks like you are asking for someone else to do your master's thesis for you.

@ijuptilk I am puzzled by your statement that you have an analytic solution for the problem since your initial condition v(z,0)=0 is inconsistent with the rest of the system.  Examine what you think is an analytical solution.  It's either wrong or it violates v(z,0)=0.

The reason that v(z,0)=0 is inconsistent is that there is no t derivative of v(z,t) in your system of PDEs, so you cannot specify an initial condition on v at t=0.

If you remove the v(z,0)=0 condition, you can obtain a symbolic solution to the problem without much difficulty.

@ijuptilk As it has been pointed out to you, sin(pi/2) is 1, so saying theta(z,0) = thetab*sin(pi/2)*z is the same as saying theta(z,0) = thetab*z.  Do you see that?

I suspect that what you really want to say is theta(z,0) = thetab*sin(pi/2*z).  Look closely at what you write. Mathematics is a very precise language.

Furthermore, are you sure you want sin(pi/2*z)?  Changing it to sin(pi/d*z) makes it compatible with the boundary conditions.

Finally, since you know the symbolic solution, why are you bothering with a numeric one?  Can you give the reason?

@ecterrab Thank you for your customary lightningly quick reaction to issues brought up here in this forum.  I will either install the Physics Update or just do `-`(1, p.q) for now.  Both methods will enable me to move forward.

Thank you again!

Rouben

@ecterrab Your explanation regarding type versus Identiry makes good sense.  With that hint I have been able to move over a good deal of my (rather extensive) old code from the LinearAlgebra vectors to Physics vectors.

I have run into a puzzle which I would appreciate if you could illuminate for me.  Consider the following code:

I don't see why Maple complains.  I can get around that by replacing the line 1 - p.q with `-`(1, p.q) but that shouldn't be necessary, or should it?

Download mw4.mw

Here is a reply to my own reply.  In the code above, under the PS, I noted that f(b_) returns [b_, 0] while it should have returned [0,b_].  Tracking down the source of the error, it turns out that it is due to the following.

So Maple considers b_ to be both a scalar and a vector!  One way to get around this is by testing b_ for Vector before testing it for scalar.  Then the outputs (1), (2), and (3) in the worksheet below are correct, but the final calculation is still problematic due to the blurring of scalar and vector zeros.

Download mw3.mw

Hello again, Edgardo,

Your response arrived as I was preparing to post an extended explanation for why I am asking the question, and why I need to distinguish between a scalar zero and zero vector.  Have a look at this:

I have been doing the equivalent of this with the LinearAlgebra package but I would rather transition to Physics[Vectors] for the reasons that you have explained .  My attempt, however, to convert everything from LinearAlgebra to Physics[Vectors] failed right near the beginning for the reason shown above.

I may be able to work around the issue by blurring the semantical differences between scalar and vector zeros, but I am afraid the resulting code will be ugly.  Your suggestion of OR(0,PhyicsVectors) seem promising.  I will try it out tomorrow and report what I find out.

Download mw2.mw

PS:  Opps, in the code above we see that f(b_) return [b_, 0].  It should have returned [0,b_].  I will have to find out why tomorrow.  It's past midnight here.

Hi Edgardo, that's excellent.  It would be good to have the documentations of that and the other Physics types available in an easy-to-find place in the help pages, although I understand that documenting 114 types would be a monumental task.

Now that I know how to check for PhysicsVectors in the arguments of a proc, I have run into a new problem.  It appears that multiplying a Physics Vector with zero results in the scalar zero rather than the zero vector.  Shouldn't there be a zero vector in the Physics package?  In contrast, in LinearAlgebra, multiplying a Vector by zero results in a zero vector, not the number zero.

The lack of the zero vector in the Physics package has the following adverse consequence:

I can't tell whether there may or may not be an easy fix for this. In any case, want to bring this to your attention.

Download mw.mw

@tomleslie Thanks for the details.  It shows that I am not just imagining things.  Sometimes the graph is colored black, even in Maple 2022 on my machines.  I need to do some more work to get to the bottom of this.

@Christopher2222 Thanks for your demo.  It shows that I am not just imagining things.  Sometimes the graph is colored black, even in Maple 2022 on my machines.  I need to do some more work to get to the bottom of this.