Is it possible to solve numerically a PDE, where the IBC is a function resulting from the numerical resolution of an ODE?

hi,

I want to setup quantum mechanical angular momentum operators and kets such that i can do something like:

Lz[2] . Ket(??, j, m) -> m hbar        (instead of getting m as eigenvalue)

L^2[1] . Ket(??, j, m) -> j (j+1) hbar^2           (instead of getting j)

where L and Lz are quantum operators. 

maybe if i knew how to do 

QuantumOp . Ket{QuantumOp, j) -> j (j+1)

i could do it with explicit tensor products of Kets - one for j, one for m?

can somebody give me an idea of how to do this, or point me at an example?

many thanks,

larry

The following product gives 0

restart;

product(1-1/k, k = 2 .. infinity);

                               0

However when I expand the product

1 - 1/2 - 1/3 - 1/4 - ... + 1/2*1/3 + 1/2*1/4 + ... + 1/3*1/4 + ... + triple products + quadruple products + and so forth...

Now the double, triple, quadruple, and so forth sums of products converge.

The 1/2 + 1/3 + 1/4 + ... nevertheless diverges, so why does maple give me 0?

Hello!
I am really desperate right now and I need help or advice.

I don't understand why dsolve doesn't work for my example. He doesn't get anything out....

restart; 
de := sin(1)*(diff(y(x), x$2))+(1+cos(1)*x^2)*y(x) = -1: 
cond := y(-1) = 0, y(1) = 0: 
dsolve({cond, de}, y(x))

Really hope for your help.

question.mw

Hello there,

I am trying to solve a pretty simple Cauchy Problem:

PDE := diff(u(t, x, y), t)+.5*(diff(u(t, x, y), x, x))+diff(u(t, x, y), x, y)+.5*(diff(u(t, x, y), y, y))+diff(u(t, x, y), x)+diff(u(t, x, y), y)+(1+(x+y)^2)*u(t, x, y) = 0

bc := u(0,x,y)=1;

with pdsolve and I get a result.

But surprisingly, Maple's pdetest applied to this result doesn't yield zero.

Hence, Maple solves my problem, but it also says that this solution is not right?

How is that possible?

Thanks a lot for your help. (btw: this is my first post here :))

Best regards,

utcyp

i have a prablem i work on it consiste of  aloop of 1000 iteration ,  and  apart of it evaluate the following sum  and integration  but maple either take very long time  about (12 hours) in evaluating it  (and it's very long )

or it get stuck . Is there any way to make maple evaluate this sum and integration  very quickely and didnt get stuck 

D

Maple 2018 memory usage increases as I try to display or manipulate the expression presented in  test_maple2018.mw. The same worksheet works perfectly in Maple 18

I've tried both in Maple 2018.1 and Command Line Maple 2018 obtaining the same result

Maple 2018.1, X86 64 WINDOWS, Jun 8 2018, Build ID 1321769

From command line maple 2018 when trying to evaluate

memory used=3.6MB, alloc=40.3MB, time=0.14
memory used=4.7MB, alloc=72.3MB, time=0.19
memory used=33.3MB, alloc=107.3MB, time=0.45
memory used=109.2MB, alloc=143.1MB, time=1.37
memory used=217.7MB, alloc=185.6MB, time=2.60
memory used=292.6MB, alloc=217.6MB, time=3.87
memory used=328.0MB, alloc=254.6MB, time=5.16
memory used=437.3MB, alloc=299.9MB, time=7.44
memory used=549.8MB, alloc=335.9MB, time=13.60
memory used=630.9MB, alloc=375.4MB, time=17.07
memory used=686.9MB, alloc=401.8MB, time=19.61
memory used=785.6MB, alloc=431.9MB, time=22.31
memory used=944.8MB, alloc=427.9MB, time=26.74
memory used=1150.1MB, alloc=427.9MB, time=32.37
Interrupted

I was wondering if my Maple 2018.1 installation is corrupted. Since I have no acces to other Maple licenses, can anyone try to execute it? test_maple2018.mw

This differential equation has an analytical solution.

However, I am looking for a numerical solution for it.

A single boundary condition with respect to t would be sufficient to solve the problem, but the command does not accept this.

In the end, I try to insert boundary conditions in relation to the variables x and t, but again this does not work.

Where am I going wrong?

Hello my friends

I have some problems with maple 18. I try to consider and extract some things about tensor such as contraction.

for instance, suppose we have metric=-exp(alpha(r))*(dt^2)+exp(beta(r))*(dr^2)+r^2*(dtheta^2)+r^2*(sin(theta)^2)*(dphi^2). how we can find all Riemann tensor and corresponding contraction, Ricci tensor and its contraction and even Weyl tensor and its contraction. unfortunately, I attempt to find them by using some other examples on the net but they don't help me to calculate them when time is the first element in coordinate, not last ( t,r,theta,phi) not (r,theta,phi)

thanks with the best regard

In Maple 2017, a simple one-liner can crash the current worksheet (in any mode with any text type it seems).

z[x]:=z

z[x]:=z(x)

Note that z and x can be any two letters, and that you can replace z[x] with the equivalent z+(ctrl shift _)+x (which displays as z_x)

I was just wondering if someone could explain why kernelopts(maxdigits) = 38654705646, as in is this different for a differing computer, or is there a design aspect of maple that requires it to be this number, or is there a mathematical reason?

I found the following inconsitencies when studying the 2nd branch of the LambertW function, and i was hoping someone can help me understand what i am doing wrong here:

#Forming an equation based on what the simplify command produces as output with the lhs on the rhs:

exp(-(1/2)*LambertW(1, 2*exp(2))+1) = simplify(exp(-(1/2)*LambertW(1, 2*exp(2))+1));

#A float approximation made directly for the first branch of LambertW directly:
exp(-(1/2)*LambertW(1, 2*exp(2))+1)=evalf[10](convert(evalf[10](LambertW(1, 2*exp(2))), 'rational'));
# A float approximation made for the value implied by equation stated in the first line gives a slightly differing value:
evalf[10](rhs(isolate((1/2)*sqrt(2)/sqrt(1/x) = convert(evalf[10](exp(-(1/2)*LambertW(1, 2*exp(2))+1)), 'rational'), x)));
#The symbolic simplify command gives the following output, which is contradictory to the evalf command's output for that argument:
exp(-(1/2)*LambertW(1, 2*exp(2))+1)=simplify(exp(-(1/2)*LambertW(1, 2*exp(2))+1),'symbolic');
#So i investigated this a little further in observing that this seemed like a few of the functions i have found very interesting, have a Number theoretic proportionality to the number of significant digits we have restricted the evalf command to:
F:=Re(exp(-(1/2)*LambertW(1, 2*exp(2))+1))+Re((1/2)*sqrt(2)/sqrt(1/LambertW(1, 2*exp(2)))):
fLOATY:=proc (k) options operator, arrow; evalf[k](F) end proc;
DATA := [seq([k, convert(fLOATY(k)*10^(k-1), 'rational')], k = 1 .. 40)];
plots[:-pointplot](DATA, color = "Black");

I'm working on a problem requiring non-commutative variables. I have this functionality working properly using the code below:

Hi all. I have two questions about polynomials over Q.

i) Let f,g be polynomials over Q. How to show (with Maple) that the decomposition field of f is included in the decomposition field of g?

ii) Let f be a polynomial of degree n  over Q with Galois group C_n, the cyclic group of order n. Then, there is a polynomial P with coefficients in Q, of degree n-1, s.t. the iteration: u0=some root of f, u_{k+1}=P(u_k) gives all the roots of f; how to find P (with Maple)?

Thanks in advance.