I want to to solve the system of partial differential equation using maple. I tried it but I am not able to solve it ... please help.

the equations are as follows

Download Finding_transformation_eqn_between_zero_and_harmonic_with_conformal1.mw

Hi 

The integration in (F2) is not work properly.

My tyr is below:

restart:with(plots):
assume(d,real):

b:=-gamma1*tau0+I*tau0*Delta-2*a*(k-1)*xr:
a:=1+I*c;
c1:=sqrt(conjugate(a))/tau0:
c2:=0.5*((conjugate(b)/sqrt(conjugate(a)))):
lambda1:=2*(1-I*d)*(t-k1)/j+(1-I*d)^2:
lambda2:=t*(1-j)*k1/j+1/sqrt(2)*(1-I*d):
lambda3:=c1*(t-k1)/j+c1*(1-I*d)+c2:
J1:=sqrt(Pi)/sqrt(2)*(1-erf(lambda2)):
J1mod:=(Re(J1))^2+(Im(J1))^2:
g1:=0.5*sqrt(Pi)*tau0*exp(c2^2)*exp(-conjugate(a)*((k-1)*xr)^2)/(sqrt(conjugate(a))):

                       
F2:=-sqrt(2)*int(exp(-x^2)*erf(sqrt(2)*c1*x+lambda3),x=-lambda2..infty);
Warning,  computation interrupted
J2:=sum(g1*J1+g1*F2,k=1..1);
J2mod:=(((Re(J2))^2+(Im(J2))^2)):
W:= unapply(no*J1mod+Omega^2*J2mod,d):
Omega:=0.01:no:=1:Delta:=0:tau0:=1:c:=0:gamma1:=0:j:=1:k1:=0:t:=2*Pi:xr:=1:
P1:=plot(W,-50..50,axes=boxed,title=tit,color=black,font=[2,3,18],thickness=2,tickmarks=[3,2],titlefont=[SYMBOL,14],font=[1,1,18],linestyle=1);

Maple seems to have difficulty calculating this integral algebraically, although it seems not excessively complicated.

int( ((-A*omega*sin(omega*x+phi)*exp(-x/tau) - A*cos(omega*x+phi)*exp(-x/tau)/tau)^2 + 1)^(1/2), x=0..t ) assuming t>0, omega>0, tau>0, A>0

any suggestions to solve this integral?

thanks in advance

Hi,

Need your help to find the convergent solution of the attached problem.

Here is some information about parameters

(0 <= gamma <= 10,      0 <= rho & nu <= 200)

Arif_Ullah.mw
 

Download Arif_Ullah.mw

Hi.

I am calculating an integral but I cannot get the result.
Can you help me.
I provide the file.

Tank you

Regards

integral_doubt.mw
 

Download integral_doubt.mw

 I'm thinking about a question about counting the total number of Eulerian trails of following graphs . 

The Seven Bridges in Gonisburg lost one bridge due to war. 

G-e₇

We looked up on Wikipedia to  add some details..

For the existence of Eulerian trails it is necessary that zero or two vertices have an odd degree; this means the Königsberg graph is not Eulerian. If there are no vertices of odd degree, all Eulerian trails are circuits. If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other. A graph that has an Eulerian trail but not an Eulerian circuit is called semi-Eulerian.

It's easy to know that G-e₇ is semi-Eulerian. So I want find all Eulerian trails. A simple attempt, found the following one in graph (Pink label).

I feel a little tricky dealing with this through Maple. The first reason is that the Maple graph theory package does not support parallel edges. Unfortunately， e₅ and e₆ are parallel edges of G-e₇.

To take a step back, what if there are no parallel edges? For considering G-e₇-e₆.

There are some built-in commands related like FindEulerianPath , but can only find a Euler circuits.

Dear friends, please I would like to ask for your help with the following problem: 

I have to compute some linear programming calculations. I thought it would be a good idea to perform them employing a parallel code. However, much to my surprise, the parallel code is slower than the single-threaded one. I enclose a worksheet sketching both codes with an example. Would you please tell me what it could be wrong with my code? 

Many thanks for your help.EXAMPLES.mws 

In this figure, y axis scale is -1, -0.5,0,0.5,1.

i need that scale -1, -0.1, -0.2 -0.3......1

how to change?

Any could you please help me to write program using for loop of 

U(0, h, m)=0 for h=1 .. 10, m=0..10.?

Hi!

If I have a list of numbers e.g, data:=[0,12,0,7,5,3,7,10,0,0,9,3,2,5,0,6]

How do I get Maple to count the values bigger or equal to seven? [ans=5]

nnnnnnnnnnnn.mwHi everyone

I am a student. I have a problem with making matrix in maple. please help me.

this is the cod that I wrote.

I uploded my cod and the picture of matrix that I want to create.

thanks

Hi,

I am trying to solve a differentiation but I think I am stuck since the solution is not what it should be.

So, I got the equation below

eq4 := `S__2 ` = sin(alpha - phi)*sin(-beta + alpha)*H^2*M/(2*sin(-beta - delta - phi + alpha)*sin(beta)*sin(alpha)) - S__1

And according to the paper I read, to get the maximum value of alpha for maximum value of S_2, I need to make differentiation to first derivative where dS_2/d(alpha) = 0

Then I should substitute back value of alpha to equation above and the paper shows that i should get equation below.

`S__2 ` = 1/2*M*K__a*H^2 - `S__2 `

where K_a is

`K__a`= [(sin(beta+phi))/((sin(beta))/(sqrt(sin(beta+delta))+(sqrt(sin(phi+delta)*(sin(phi-varepsilon)))/(sin(beta-varepsilon))))]

I know its really hard but hope someone can give some idea how to do it.

Thank you very much.

Kind regards

Faiz Farhan

Hi. Can someone solve for w as a general function of k, without RootOf

w^3+3w^3*(1-w)+6w^3*(1-w)^2=k, k constant

i tried

allvalues(solve(w^3+3*w^3*(1-w)+6*w^3*(1-w)^2-k,w))

and also with option explicit (edit)

Dear all, 

Would you allow me to ask a question?

What would be a way to re-write the 'eq2' in the following worksheet as 'eq_given'? The check, 'is...'. shows that two expressions are the same. 

Thank you, 

Download Q20200817.mw