Unanswered Questions

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Hi,

I would be really grateful if someone can help me in solving the below attached problem in maple.

Thanks in advance.

Plot the wedge cut from the cylinder x²+y²=1 by the planes z=-y and z=0.

Hey everyone,

f_1 and f_2  are satisfying the set of non-linear integral equations I have attached to this message.
I know that I need to solve them numerically by iterations. Probably, the first guest of the function f_1 and f_2  is the driving term. a is just a parameter which can be fixed (I guess smaller than \pi/4). * is the convolution product and k is the momentum space parameter. I learnt that in order to solve them I should solve them in the Fourier space. I know also that I need to discretize these function in the “real ” space between {-L,+L} before applying the FFT or one of its relatives. Thank you for any suggestions or leads.

Hi,

I noticed that, in Maple 2020.2, the caracters seem smaller. As if the zoom had somewhat been reduced (a bit).

However, in the preferences, the default zoom level I would like is between 100 and 125% (something like 110%) (since the default zoom level is adjusted by steps of +/- 25%). I wondered if there was a way to set the default zoom level to an arbitrary value. In fact I thought it would be great to have a field instead of a list of choices, so we can choose a custom value.

Thank you

Here is my try to integrate the expression L with trapozoid or simpson 

numerical_int.mw

 

restart;
V:=x->piecewise(0<=x and x<=a,0,infinity):
ic:=f(x,0)=piecewise(0<=x and x<=a,A*x*(a-x),0):
pde :=I*h*diff(f(x,t),t)=-h^2/(2*m)*diff(f(x,t),x$2) +V(x)*f(x,t):
sol:=pdsolve([pde,ic],f(x,t)) assuming a>0;
Latex(sol)

gives

f \! \left(x , t\right) = 
\left(\left\{\begin{array}{cc}A x \left(a -x \right) & 0\le x \le a  \\0 & \mathit{otherwise}  \end{array}\right.\right)+\left(\Mapleoverset{\infty}{\Mapleunderset{n =1}{\textcolor{gray}{\sum }}}\! \frac{t^{n} \left(\textbf{proc} (U) \\
\textbf{option} \,operator,\,arrow; \\
\mapleIndent{1} r-1 st I \ast (-1/2 \ast h\hat{~}{2} \ast m\hat{~}{-1} \ast \mathit{diff} (\mathit{diff} (U,\,x),\,x) + \mathit{piecewise} (0&lex \, \textbf{and} \, x&lea,\,0,\,infinity) \ast U) \ast h\hat{~}{-1}\\
\textbf{end\ proc};\right)^{\left(n \right)}\! \left(\left\{\begin{array}{cc}A x \left(a -x \right) & 0\le x \le a  \\0 & \mathit{otherwise}  \end{array}\right.\right)}{n !}\right)

Notice, non-printable characters. I think it should have been \ast there but it gives  st

Maple 2020.2 and Physics 897.

FYI, this is what latex() command gives


latex(sol)

f \left( x,t \right) =
\begin{cases}Ax \left( a-x \right)  & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases}
+\sum _{n=1}^{\infty }{\frac {{t}^{n} \left( U\mapsto {\frac {-i
\begin{cases}0 & 0\leq x \land x\leq a\\\infty  & \text{otherwise}\end{cases}
U}{h}}^{ \left( n \right) } \right)  \left( 
\begin{cases}Ax \left( a-x \right)  & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases}
 \right) }{n!}}

Which compiles with no problem

\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
\[
f \left( x,t \right) =
\begin{cases}Ax \left( a-x \right)  & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases}
+\sum _{n=1}^{\infty }{\frac {{t}^{n} \left( U\mapsto {\frac {-i
\begin{cases}0 & 0\leq x \land x\leq a\\\infty  & \text{otherwise}\end{cases}
U}{h}}^{ \left( n \right) } \right)  \left( 
\begin{cases}Ax \left( a-x \right)  & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases}
 \right) }{n!}}
\]
\end{document}

 

Thank you

Dear all

I have  Lie commutations for vectors e1, e2, e3, e4, e5, e6 as follow:

[e1, e3] = e3, [e1, e4] = e4, [e1, e5] = e5, [e1, e6] = e6, [e2, e3] = -e5, [e2, e4] = e6, [e3, e5] = e6

for which the command 

Query("Jacobi")

returns the false result, which means, the vectors are not closed under Jacobi's identity. How can I find vector triplets for which Jacobi's identity does not hold?

Please find Maple file.Jacobi_identity.mw

Dear all, 

I have a time-fractional PDE as follows.  ( denotes Caputo fractional derivative with respect to t) 

for alpha=1, this is a classical PDE and the exact solution is given as follows (in a book)

 

Question: 

 

1) for alpha=1, I want to find the L2 errors and L∞ errors in a table. 

2) for alpha=0.5, Can Maple find a solution (numeric or exact)?

 

MY TRY: (MAPLE 2020.2)

download the code.mw

restart:
with(plots):
PDE:=diff(y(x,t),t)=y(x,t)*diff(y(x,t),x$3)+y(x,t)*diff(y(x,t),x)+3*diff(y(x,t),x)*diff(y(x,t),x$2) ;


#c is an arbitratry constant
c:=4:
exact_sol:=(x,t)->-8*c/3*(cos ((x-c*t)/4))^2;

# I selected initial and boundary conditions as follows
IBC := { y(x,0)=exact_sol(x,0),y(0,t)=exact_sol(0,t),D[1](y)(0,t)=D[1](exact_sol)(0,t),y(1,t)=exact_sol(1,t)};
 	
numeric_sol := pdsolve(PDE,IBC,numeric);

num3d:=numeric_sol:-plot3d(t=0..1,x=0..1,axes=boxed,
            color=[0,0,y]);
exact3d:=plot3d(exact_sol(x,t),t=0..1,x=0..1,axes=boxed);
display(exact3d,num3d);

pdetest(y(x,t)=exact_sol(x,t),PDE,IBC);


Hi

I have a system of pde that it is solved with pdsolve procedure.

This procedure takes a few time, but when I need to do plots, especially 3d plot the software takes a lot of time (several hours).

How can I make plots faster?
Thanks.

It's been about a year since I've been able to display any worksheet at all on MaplePrimes. In the example below, I took a very simple worksheet that had been displayed in an Answer to another recent Question and tried to upload it. So, we know that it's somehow possible to display this particular worksheet on MaplePrimes.

Maple Worksheet - Error
Failed to load the worksheet /maplenet/convert/prove.mw .
Download prove.mw

Given a metric, to compute quantities in the NP formalism one needs to specify a null tetrad. In the various examples in the help pages, sometimes the tetrad is specified simply as a list of 4 vectors, e.g., NT := [...] and sometimes evalDG is applied as in NT := evalDG({...]). Using the first format, Maple accepted NT as argument in NPSpinCoefficients but  NPCurvatureScalars(SpinCoefficients,NT) complained that the second argument wasn't a list of four vectors. When I used the second format, both commands returned the expected results. Why the difference?

RobinsonTrautmanSpinDG.mw

I am facing difficulty to realize this double iterative process. 

The equations in question are