Maple 17 Questions and Posts

These are Posts and Questions associated with the product, Maple 17

Dear all
I have an algorithm  to solve a first order odes, all steps of the algorithm ( as presented in the book are coded) but unfortunately something wrong. 
The algorithm and the code are attached in the following code. 
Thank you in advantage for your help. 

sol_odes.mw

Hello friends, I have the following problem:
I have two lists of vectors, L1 and L2. The lists have the same number of vectors, and all the vectors have the same length.
I need to check if there is a permutation that, when applied to all the elements of one list, will obtain all the elements of the other list. For example, consider the following lists :

L1:=[<0|0|0>,<2|1|2>,<1|2|1>];
L2:=[<1|1|2>,<2|2|1>,<0|0|0>];

In this example the vectors are of length 3. Therefore, there are 3!=6 possible permutations. Namely:

P1:=<<1,0,0>|<0,1,0>|<0,0,1>>;
P2:=<<0,1,0>|<0,0,1>|<1,0,0>>;
P3:=<<0,0,1>|<1,0,0>|<0,1,0>>;
P4:=<<0,0,1>|<0,1,0>|<1,0,0>>;
P5:=<<0,1,0>|<1,0,0>|<0,0,1>>;
P6:=<<1,0,0>|<0,0,1>|<0,1,0>>;

In this case there are two permutations that satisfy the condition above, namely:

P3:=<<0,0,1>|<1,0,0>|<0,1,0>>;
P6:=<<1,0,0>|<0,0,1>|<0,1,0>>;

Cause

for i in L1 do Multiply(i, P3) end do;
>[0 0 0]
  [2 2 1]
  [1 1 2]
 
The same result is obtained using the permutation P6.
I'm working with larger lists and longer vectors so I'm looking for a quick way to check this. Thanks for your valuable help.

Hi all,

I want to verify the sum of associated Laguerre polynomials as shown in the picture below. I have tried numerical, but I am struggling with the syntax.

Anyone know how to do that?

Dear all
My goal, is expand a given function using chebyshev polynomails. Everything is well written, but unfortynattely, the coeffients an, are not computed exactly, but the result return only integral form and there is evalaution of this integral.

How, can I expand my function f , using sum ( a_n chebyshev Tn), for x in [0,1] and we get explicitely the results. 

Question_integral_chebyshev.mw

Thank you for any help 

Dear all;

I have a data, I would like to save this data in a table with labeled columns and  each column contains the corresponding values.

cretae_tabl.mw

thank you for your help 

Dear all

I would like to compute the monomial polynomial in taylor series, I tried 
f:=cos(t);

fn:=n->subs(diff(f(x),x$n),x=0)/factorial(n);
but it is does not work 
anay help please

Dear all

I solve a first order nonlinear ode, using dsolve but there is no solution obtained.

problem_dsolve.mw
How, can I get the exact solution.

tahnk you for your help

Dear all

I compute the solution of first order nonlinear ode, supplied to initial condition.

The code is written, the exact solution is derived.

 plot the solution in a small interval like (0,1/5) I see that there is no difference between exact and semi-analytical soluton.

But, If I plot the solution in other interval like (0,1) or (0,2), It is noticed that the semi-analytical solution is different to the exact solution. 
Thansk you in advance for your help 

test3.mw

Hi

I got the error like this unable to convert to an explicit first-order system

please anyone can help me to solve this

I am attaching the worksheet

with(plots); restart

eq1 := (2*eta*gamma+1)*(diff(f(eta), `$`(eta, 3)))+2*gamma*(diff(f(eta), `$`(eta, 2)))+f(eta)*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0;

(2*eta*gamma+1)*(diff(diff(diff(f(eta), eta), eta), eta))+2*gamma*(diff(diff(f(eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0

(1)

eq2 := (diff(F(eta), `$`(eta, 2)))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0;

(diff(diff(F(eta), eta), eta))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0

(2)

eq3 := (2*eta*gamma+1)*(1+Rd)*(diff(theta(eta), `$`(eta, 2)))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0;

(2*eta*gamma+1)*(1+Rd)*(diff(diff(theta(eta), eta), eta))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0

(3)

eq4 := 2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0;

2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0

(4)

bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0

(5)

params := [Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1];

[Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1]

(6)

sol := dsolve(eval([eq1, eq2, eq3, eq4, bcs], params), numeric, output = array([0]), maxmesh = 5000, initmesh = 1000)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

``

Download MapleOde.mw

I wrote the following orders

With(GeM):
gem_decl_vars(indeps=[t,x], deps=[u(t,x)]);
gem_decl_eqs([diff(u(t,x),t,t)+a∗diff(u(t,x),x,x)+b∗
u(t,x)+c∗(u(t,x))^3=0],solve_for=[diff(u(t,x),t,t)])

det_eqs:=gem_conslaw_det_eqs([t,x,u(t,x),diff(u(t,x),
t),diff(u(t,x),x)]):
CL_multipliers:=gem_conslaw_multipliers();
simplified_eqs:=DEtools[rifsimp](det_eqs,
CL_multipliers, mindim=1)

in maple 17, but the program cannot calculate and gives me an error. Does anyone help me to solve this problem.


 

.

Dear all
Dear all, is  there any Maple code available to solve the heat  two dimensional heat equations using Rk4. The second derivative will be replaced using Finite difference, so that we get a linear system of odes.  
Thank you for any help 

Hi!

I have created a procedure for the so-called "Chaos Game" for the generation of Fractals. The file is the following:

Fractals_ChaosGame.mw

On the other hand, for a given day set D:={(x0,y0,(x1,y1),...., (xN,yN)}, for simplicity we assume D is contained in [0,1]x[0,1], one can to construct an "Iterated Functions System" such that its attractor set contains the set D. A detailed exposition of this topic can be found in the famous Barnsley's book "Fractals Everywhere". Also, in the following paper (sections 2.5 and 4-A):

https://arxiv.org/pdf/2102.09855.pdf

I have tried to implement in Maple 17 a procedure to create such Iterated Function System:

IFF_v2.mw

But, I feel that there is something wrong...After plot (with the Chaos Game procedure) a lot of points of the Iterated Functions System (i.e., an approximation of its attractor set), I have a "set of points", instead of a figure similar to a curve (which I feel that must be the correct).

Please, Somebody can have a look to the attached files?

Many thanks in advance for your comments.

How to solve these systems of BVP and obtain values for gamma term.

Dear all

I have a second order PDE, i used pdesolve but no solution obtained, why?

pdsolve_pde.mw

thanks

 

 

 Pictures on the theme of Klein bottle.  Wikipedia article
KL_B_1.mw

KL_B_2.mw

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