Hello there, 

When I tried to solve an equation using the 'solve' command in Maple, I got an answer. 

However, I could not understand how Maple got to the answer. Would you tell me what steps Maple might have gone through in order to come to the answer?

Here is my worksheet:

q20210130.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/q20210130.mw .
 

Download q20210130.mw

PS) Perhaps this editbox began to dislike Google Chrome.

Dear Maple Users,

I appreciate your help with the previous 1D PDE problem that I posted.

Now I have another 2D axisymmetric diffusion PDE, looking for u(r,z,t), no variation in the theta direction:

PDE: u'_t = alpha*(u"_r + (1/r)*u'_r + u"_z); a < r < b, 0 < z < L, 0 < t < infinity

BC1: u| _{z = L} = Psi_s

BC2: -alpha*u'_z| _{z = 0} = 0

BC3: -alpha*u'_r| _{r = a} = 0

BC4: -alpha*u'_r| _{r = b} = flux_b

IC: u(r,z,0) = (z/L)*Psi_s

a, b, L, alpha, Psi_s, flux_b are given.

My attempt at a solution is attached, following the solution path that you provided for the previous 1D PDE problem.

2D_CCS_PDE_Sol.mw

I have run into an error message that I am unable to resolve. I would greatly appreciate your taking a look at this.

Perhaps, there is no closed form solution to this problem and a numerical solution may have to be attempted.

Please advise. Thanks.

Joseph Thodiyil 

How do I print the body of a procedure.  In older versions, verboseproc controlled this.

restart

interface(verboseproc = 3)

interface(prettyprint = 1)

print(int)

                  _m140116321288416, [_m140116321288416]

print(type);
                 proc () option builtin = type; end proc,

                   [proc () option builtin = type; end proc]

Can I make something like it using codegen (dinamically set parameters and default arguments freely)?
proc( a , b::integer , c:=0 , d::integer:=1 , { e:=2 , f::integer:=3 } ) return a, b, c, d, e, f end proc

eq1 := diff(h(t), [`$`(t, nu)])+(1/4)*h(t) = 8/3*(1/(sqrt(Pi)*t^(1/2))-(3/32)*t^2+(3/16)*exp(-t)-1);

with ics h^k (0)=0 for k=0..n

Dear Maple Users,

This particular question is example problem 8.4.1 in the textbook: "PDE & BVP with MAPLE", 2nd Edition by George A. Articolo.

I shall paraphrase the problem here and attach the Maple Worksheet solution as detailed in the textbook.

We seek the temperature distribution u(x,t) in a thin rod whose lateral surface is insulated over the interval I = {x | 0 <x<1}. The left end of the rod is held at a fixed temperature of 10, and the right end is held at the fixed temperature of 20. There is no internal heat source. The thermal diffusivity of the rod is k = 1/20, and the rod has an intitial temperature distribution u(x,0) = f(x) given as follows.

The nonhomogeneous diffusion equation is:

u_t'(x,t) = k*u_x"(x,t) +h(x,t)

The BCs are nonhomogeneous:

u(0,t) = 10

u(1,t) = 20

The IC is:

u(x,0) = 60x -50x²+10

The internal heat source term is:

h(x,t) = 0

I have typed in the MAPLE commands exactly as in the textbook (attached), but it does not execute in my Student 2020 version of MAPLE.

Could you please take a look at the attached MAPLE worksheet and let me know if something can be done to make it work.

Thank you for your help.

Joe Thodiyil

George_A_Articolo_2ndEdition_Ex_8.4.1_PDE.mw

Dear all

I solve a given pde with some conditions given, but I get 

unable to handle PDE problem subject to boundary conditions 

solution_pdes.mw

many thanks for your help

I am trying to find one option so that  a sphere is tangent with every edge of a tetrahedron. Suppose tetrahedron OABC, here O(0,0,0), A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3).  How to find a sphere is tangent with every edge of a tetrahedron?

I know how to contruct an isoscele ABCD trapeze knowing the 2L length of AB and BC=CD=CD=a. But I don't know answer to that question : L being fixed together with points A and B , show that the place of C when a varies is a branch of hyberbola. Here is my code.

restart; unprotect(O, D);
with(plots):
Vdot := proc (U, V) add(U[i]*V[i], i = 1 .. 2) end:
dist := proc (M, N) sqrt(Vdot(expand(M-N), expand(M-N))) end:
_EnvHorizontalName := x: _EnvVerticalName := y:
O:=[0,0]:A:=[-L,0]:alpha:=arccos((2*L-a)^2/(2*a*(2*L-a))):h:=tan(alpha)*(2*L-a)/2:
B:=[L,0]:C:=[L-(2*L-a)/2,h]:D:=[-L+(2*L-a)/2,h]:
L := 6; a := 7;
poly := [A, B, C, D, A];tp := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"]], color = black, 'align' = {'above', 'right'});
trapeze := polygonplot(poly, axes = normal, color = "DarkGreen", transparency = .9);
display([tp, trapeze], scaling = constrained); Thank you foryour help.

Hi everyone:

I want to write the below serie in Maple, how can I do it?

where: k = 0,.....,n

n is a Natural number.

tnx...

Dear Users!

I want to find the solution of the solution of PDEs as given bellow:

restart;
PDE1 := diff(u(y, t), t)+diff(u(y, t), t, t) = diff(u(y, t), y, y)-u(y, t);
PDE2 := v(y, t)+diff(tau(y, t), t) = diff(u(y, t), y);
ICandBC := {tau(y, 0) = 0, u(0, t) = 0, u(3, t) = 0, u(y, 0) = 0, (D[2](u))(y, 0) = 0};
pds := pdsolve({PDE1, PDE2}, ICandBC, numeric);

But got the following error

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same
Kindly help me to fix this error. I shall be very thankful. 

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

I have created a set of help files using the example templates. After I create the .help file and install it with my package, I can view the help pages in the help viewer. However, when I click on any link within a help page, the target page opens as a worksheet in Maple. I understand this is because I created the hyperlink with a worksheet as the target. However, I don't know where to obtain the help topic name for a help page before it has been created.  I have searched help, but can't find any applicable guidance.  Can anyone tell me how to determine the help topic name when first creating the help pages.

I have attached one of my help file worksheets.     Hlpdiracmatrices.mw

Hello,

I defined a vector (in cartesian coordinates) with Physics[Vectors] as

q_:=3 _i + 5 _j + 2 _k

Then I wanted do a transformation on this vector by multiplying it with matrix

M:=<3,4,2|5,6,2|2,1,4>
M.q_

However, I am getting a result where every element of the matrix is multiplied by the vector.

If I define q as <3,5,2> then matrix multiplication works as one would expect.

So, my question is how can I have a matrix multiplication with a vector defined with Physics[Vectors] package?

Dear Maple community,

I would really appreciate it if you could tell me how I can solve numerically in Maple the following system of equations (the Maple file containing these equations can be found here: Mapleprime_Q.mw):

Thank you very much in advance for you help!

Hello,

When I create a vector in spherical coordinates and map it to cartesian coordinates with Physics[Vectors] package as follows,

restart:with(Physics[Vectors]):
q_:=a _r + b _theta + c _phi
ChangeBasis(q_,cartesian)

I get the answer:

(a*cos(phi)*sin(theta)+b*cos(phi)*cos(theta)-c*sin(phi)) i + (a*sin(theta)*sin(phi)+b*cos(theta)*sin(phi)+c*cos(phi)) j + (-b*sin(theta)+a*cos(theta)) k

which is what I would expect.

But if I try to do that with VectorCalculus package as follows,

q := SetCoordinates(<a, b, c>, spherical)
MapToBasis(q, cartesian)

This gives 

(a*sin(b)*cos(c)) ex + (a*sin(b)*sin(c)) ey + (a*cos(b)) ez

I am confused about this!

The SetCoordinates(<a, b, c>, spherical) command outputs

q:=(a) er  + (b) ephi + (c) etheta

here, a,b, and c are  depicted as the components of the vector q in spherical coordinates, but when I map to cartesian coordinates, a,b, and c are treated as if they were the coordinates in spherical coordinates rather than components-- unlike ChangeBasis in Physics[Vectors] package.

Why are these two different?