Dear Support

I am attempting to model quantum dynamics, and have defined a coupled set of nonlinear PDEs I would like to solve for coupled solutions u(x,y,t) and v(x,y,t) using MAPLE 18.

I attach an image of part of the worksheet the pair of PDEs...The initial conditions u(x,y,0), v(x,y,0) are a pair of respectively positive and negative 2D gaussians on the x,y, domain.

Before I go any further, please would you check that MAPLE 18 is in principle capable of finding solutions u(x,y,t), v(x,y,t) solutions, and let me know whether it is worth pursuing the solution?  I have had a look at the MAPLE documentation, but am not sure whether MAPLE can solve this system.

As a warm-up, I successfully solved a 1-D system u(x,t), v(x,t) using pdsolve[numeric], but I am not clear whether MAPLE 18 can solve for u(x,y,t), v(x,y,t) either numerically or analytically on the [x,y,t] domain.

I hope you can provide help/guidance. An image the equations in MAPLE is displayed here...

Melvin Brown

UK

Forgive me for asking but I can't seem to find it in the docs, how do I create a plot which has a categoric variable rather than just real ones? i.e. having it print string labels along one axis rather than integers..

Also hoping this is possible on a 3D graph where each category is associated with 2 real values, i.e. a slice of the 3D plot...

Thanks

 Anyone can explain to me this program using Runge Kutta fourth order method

Download program.mwprogram.mw

Anyone can explain to me the Runge Kutta method using the following equations and conditions??

diff (diff (diff (f (eta), eta), eta), eta)+ f (eta)* diff (diff (f (eta), eta), eta)=0

diff (diff (theta (eta), eta), eta)+ f (eta)* diff (theta (eta), eta)=0

f(0) = 0, (D(f))(0) = 0, (D(f))(5) = 1

theta(0) = 1, theta(5) = 0

In DifferentialGeometry package, let P be the output of Prolong applied to a Transformation.

How to extract each identity/equation from P?

Is there a way to convert P to an array of equations?

I am learning how to use dchange in Maple. I can do  something as dchange(x=t^2) OK, but I need to do dchange(x=t^n) where "n" is meant to be a parameter that I can later use subs on to set it to any number I want.  But I do not know how to tell Maple that "t" is the new variable and that "n" is meant to be used as constant or parameter.

As an example, this works

n:=2;
ode:=x^2*diff(z(x),x)=0;
PDEtools:-dchange({x=t^n},ode,{t})

But this does not work

n:='n';
ode:=x^2*diff(z(x),x)=0;
PDEtools:-dchange({x=t^n},ode,{t});
subs(n=2,%)

It used "n" above as new variable. So the dependent variable which was z(x) became z(t,n). 

So I need to tell Maple that "t" is the new variable only and not "n" as well. 

Is it possible to do this in Maple?

Maple 2019 on windows.

Hi,

I compute a double integral, and I would like to change the order of integration ( of course we take into account the domain of integration, that must be changed), but unfortunately I have two different values instead the same value.

order_integration.mw

Note that I the code if I put t_0=0, I get the same value. Bur for other values of t_0, i havent the same value.

Many thanks for your help

Maple gives me the incorrect answer to the hundredth place. (arithmetic.mw)

>15000*(1+.06/365)^(10*365)
>                        27330.47804

I tried using an exact fraction 15000*(1+(6/100)/365)^(10*365) as well.

How can I draw together the function f(x,y)=(x.y^2)+1 and its tangent plane at the point (2,1,f(1,2)) in each of the following rectangles? 

(Note that the equation of the tangent plane at the given point is z=x+4y-3)

a. 2<=x<=3 and 1<=y<=3

b. 2<=x<=2.1 and 1<=y<=1.2

c. 2<=x<=2.01 and 1<=y<=1.02

I can  this equation.

CV.mw
 

Download CV.mw

Greetings everybody!

I am facing a strange problem. Dissolve/numeric seems to provide a solution and gives no error. However, when I try to plot the solution, Maple gives an error. Please guide me how to get rid of this error and how to plot the graph?
Please see the attatched file.

Thanking in anticipation. 

fracmprime.mw

with(Groebner);

Jugdement := proc (F, P)

local f, N1, N2, i, j, k, q, LTF, LTPj;

N1 := nops(F); N2 := numelems(P);

for i to N1 do

LTF := LeadingTerm(F, plex(w, t, s, x, y, z));

for j to N2 do

LTPj := LeadingTerm(P[j], plex(w, t, s, x, y, z));

f := divide(LTF[2], LTPj[2], 'q');

if f = true then

k := j;

break

end if

end do;

if f = true then

break

end if;

if f = false then

F := F-LTF[1]*LTF[2]

end if

end do;

return k, f, q, P[k], LTF[1]

end proc：

F := x^2+y^2+z^2;
                             2    2    2
                       F := x  + y  + z 
P := {z, x*z, y*x};
                       P := {z, x z, y x}
Jugdement(F, P);
Error, (in Jugdement) illegal use of a formal parameter

I want to know what is the problem?

i) D(X,Y) , D(X,Z) ,D(Y,Z) COVARİANT DERİVATİVE ?

İİ) [X,Y] LİE OPERATOR ? 

İİİ) R(X,Y)Z = D_x  D_y Z - D_y D_x Z - D[X,Y] Z

How to improve menu speed in Maple 2016?

I am using Maple 2016, when I right click the equation, it really takes a long time to show the menu. It seems that the CPU usage and Memory usage is low, it should be fast as it is only a showing menu action, what's wrong with that?

Hi,

The help page TimeSeriesAnalysis, ExponentialSmoothingModel contains an error.
The command that generates the output (7) should be
esm2 := ExponentialSmoothingModel(seasonal={"A","M"},constraints=admissible)
instead of
esm2 := ExponentialSmoothingModel(seasonal={A,M},constraints=admissible)

PS : there is no tag relative to TimeSeriesAnalysys

Hello! How would I do the following question using the maple program? I am not sure about the syntax. Thank you!

Express (cos^6)*t in terms of cosines and sines of multiples of t for

(cos^6)*t = a*cos(6*t) + b*cos(4*t) + c*cos(2*t) + 5/16

Where a = ?, b = ?, and c = ?