dear all
I would like to solve the following differential equation in Maple Numerically.

restart;
pde := I*10*diff(u(k, t), t) + (diff(u(k, t), t, t)) -16* u(k, t) = 0;
ics := u(k, 0) = sqrt(Pi/2)*csch(Pi/2*k), (D[2](u))(k, 0) = -(1/4)*sqrt(2)*Pi^(3/2)*csch((1/2)*Pi*k)*coth((1/2)*Pi*k)
bcs := u(0, t) = 0, u(100, t) = 0;
sol := pdsolve(pde, {ics, bcs}, numeric, range = 0 .. 1, output = listprocedure);
sol;

here the sech(x)^2 in real space and corresponding fourier transformaation is the initial condition

the Gaussian function as initial condition is also an alternative.

How can I solve it?

Hello, I am trying to evaluate this summation, but it keeps giving me a "Error, (in H) bad index into Vector", I can`t find the problem in function, would somebody helps? thanks.

My function:

with(linalg); H := proc (z, aa, AA, bb, BB, m, n, p, q) mu0 := sum('BB'[i], i = 1 .. q)-(sum('AA'[i], i = 1 .. p)); beta0 := (product('AA'[i]^(-'AA'[i]), i = 1 .. p))*(product('BB'[i]^(-'BB'[i]), i = 1 .. q)); if z <> 0 and 0 < mu0 or 0 < abs(z) and abs(z) < 1/beta0 and mu0 = 0 then do s := Vector([seq(-('bb'[i]-v)/'BB'[i], i = 1 .. m)]); Hz := sum(sum((product(('`if`')(i <> h, GAMMA('bb'[i]+'BB'[i]*'s[h]'), 1), i = 1 .. m))*(product(('`if`')(i <> h, GAMMA(1-'aa'[i]-'AA'[i]*'s[h]'), 1), i = 1 .. n))*(-1)^v*z^(('bb[h]'+v)/'BB[h]')/(('`if`')(m < q, product(('`if`')(i <> h, GAMMA(1-'bb'[i]-'BB'[i]*'s[h]'), 1), i = m+1 .. q), 1)*`if`(n < p, product(('`if`')(i <> h, GAMMA('aa'[i]+'AA'[i]*'s[h]'), i = n+1 .. p), 1), 1)*factorial(v)*'BB[h]'), h = 1 .. m), v = 0 .. 10) end do end if; return Hz end proc

>evalf(H(.547, Vector([-23-j]), Vector([.5]), Vector([0, -24-j]), Vector([1, .5]), 1, 1, 1, 2))

Hello,

I am trying to solve the self similarity problem for external natural convection which is the following coupled problem

•     3/4*F(eta)*Theta(eta)'  = Theta(eta)''
•     1/2 (F(eta)')^2 - 3/4 F(eta)*F(eta)'' = Pr*(Theta(eta) - F(eta)''')

where Pr is a constant and  ()' denotes differentiation with respect to eta. The boundary conditions are:

•     at eta = 0, F = 0, F'=0, Theta = 1
•     at eta -> infinity, F' = 0, Theta = 0

I tried the following but I cannot obtain a solution

Download wip.mw

How does this happen, that is, what is the algorithm failure here? 

for L in [[4, 2], [8, 5], [9, 2], [16, 14], [25, 2]] do
traperror(MinimumPermutationRepresentationDegree(SmallGroup(op(L))))
end do;

I have been unable to add a directed light source to my plot3d drawings.  Perhaps I am misreading the documentation.  In the following experiment, I attempt to shine a red light from the direction (phi,theta) but changing the values of phi and theta don't seem to change the scene's lighting.  Can you change the lighting in your Maple?

restart;
with(plottools):
with(plots):
Explore(display(sphere(), style=surface, color=yellow, light=[phi,theta,1,0,0]),
	phi=0..Pi, theta=0..Pi);

The documentation shows that one can set up custom latex form for different function/variables: 
https://www.maplesoft.com/support/help/maple/view.aspx?path=latex/functions

This is very nice, but how do I see what's currently set? 

I was hoping something like:
showstat(`latex/AntiCommutator`); 
or 
eval(`latex/hypergeom`); 
would work, but these don't.

I would like to simply copy/paste what maple already does and only make slight adjustments - don't want to have to write these from scratch. 

thanks!

How to remove the ln(e) in the fianl answer shown in the picture, ( must be Maple 15), thanks

Hi,

I want to solve system of PDE equations by maple and i dont know how can i write it codes that can solve them for me. Can you create the code for the equation

Thank you

restart;
with(geometry):
with(plots):
_EnvHorizontalName = 'x':
_EnvVerticalName = 'y':
point(A, [-2, 7]):
point(B, [-5, -2]):
point(C, [8, -2]):
triangle(ABC, [A, B, C]):
display([draw[A(color = black, symbol = solidcircle, symbolsize = 6), 
               B(color = black, symbol = solidcircle, symbolsize = 6), 
               C(color = black, symbol = solidcircle, symbolsize = 6), 
               ABC(color = blue)], 
         textplot([[coordinates(A)[], "A"], 
              [coordinates(B)[], "B"], 
              [coordinates(C)[], "C"]],
              align = [above, right])], 
              axes = none);
Would you explain to me why this error ? Thank you.
Error, (in plots:-display) expecting plot structures but received: [geometry:-draw[A(color = black, symbol = solidcircle, symbolsize = 6), B(color = black, symbol = solidcircle, symbolsize = 6), C(color = black, symbol = solidcircle, symbolsize = 6), ABC(color = blue)]]

Edits: In fact it is a set partition problem.

I have the following subsets: 

s:={"a","b","c","d","e","f"}:

I want to divide the set into 2 groups such that each group has exactly 3 elements. We want to generate all solutions. Note that we treat ({"a", "b", "c"}|{"d", "e", "f"}) and ({"d", "e", "f"}|{"a", "b", "c"}) as the same solution.

So first I used the choose function to generate all 3-subsets and then filtered for duplicate solutions.

with(combinat):
M:=[op(choose({"a","b","c","d","e","f"},3))]:
l:=[ListTools:-Categorize((x,y)-> is(x =`minus`(s, y)),M)]:
seq(l[i][1],i=1..10)

{"a", "b", "c"}, {"a", "b", "d"}, {"a", "b", "e"}, {"a", "b", "f"}, {"a", "c", "d"}, {"a", "c", "e"}, {"a", "c", "f"}, {"a", "d", "e"}, {"a", "d", "f"}, {"a", "e", "f"}

But I feel like the solution is a bit inefficient. In fact, we only need half of all 3-subsets. I wonder if we can only keep one representative member of the same  solutions when generating the 3-subsets. 

gengcuts.mw

 In fact, the problem can be generalized as follows: given a list of n elements, divide it into m groups and generate all solutions. Similarly,  the same solution is generated only once. 

Why there is an error? Is any part missing in the if statement?

Download maxnmin.mw

I input this codes:

latex((4*n-1)/9-7/16*n)

\frac{n}{144}-\frac{1}{9}

This is not the output I expected.  I would like to obtain an expression similar to the one below.

\frac{4 n-1}{9}-\frac{7}{16}n

How can I achieve this, as Maple seems to have processed it internally.

Does maple over-understand the expression.

Good day,
 

1. Please I need your greatest help. Can anyone please help me to run the examples on the attached papers on Maple software?

 2. Also help me to plot the graphs along with the exact solution

 3. If possible with tables

 I tried but did not get the results as expected. I shall be very grateful if I can get assistance from you

Thanks
 

How to perform PCR principal component Regression and PLS partial least squares Regression in Maple?

Dear all

have a nice time. 

I have a system of nonlinear differential equation with continuous delay.  I tried to find some books that define a strategy to compute the characteristic equation but unfortunattely the most of papers or books give directly the formula without any proof. 

I tried with maple, but unfortunattely no solution up to now. 

I hope find the strategy how find the characteristic equation of the attached system.

characteristic_equation.mw

thanks