Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

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

I can  this equation.

CV.mw
 

restart; c__v := 1.2; `τ__q` := 8.5*10^(-12); `τ__T` := 90.0*10^(-12); rho := 1000; k := 10

1.2

 

0.8500000000e-11

 

0.9000000000e-10

(1)

k*(diff(T(x, t), x, x))+k*`τ__T`*(diff(T(x, t), t, x, x)) = rho*c__v*(diff(T(x, t), t))+(diff(T(x, t), t, t))*c__v*rho*`τ__q`+(1/2)*c__v*rho*`τ__q`^2*(diff(T(x, t), t, t, t))

10*(diff(diff(T(x, t), x), x))+0.9000000000e-9*(diff(diff(diff(T(x, t), t), x), x)) = 1200.0*(diff(T(x, t), t))+0.1020000000e-7*(diff(diff(T(x, t), t), t))+0.4335000000e-19*(diff(diff(diff(T(x, t), t), t), t))

(2)

Boundary condition:

T(0, t) = 300; T(10, t) = 300

#####################################

INITIAL CONDITIONS:

 

T(x, 0) = 300; (D[1](T))(x, 0) = 0, (D[2](T))(x, 0) = 0

(D[1](T))(x, 0) = 0, (D[2](T))(x, 0) = 0

(3)

``


 

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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!
  As we  known, in Graphtheory , a loop is an edge that joins a vertex to itself (for example  fig1 vertex1) and multiple edges (for example Fig2)are two or more edges that join the same two vertices.  But in Maple,  G := Graph({{a, b}, {a, c}, {b, c}}). The Edges(G) function returns a set  (not list )of the edges of G.  So, for example I can't create loop{1,1} by G:=Graph({{1,1},{1,2},{1,5},{2,5},{2,3},{5,4},{3,4},{4,6}})   . But in my research, I consider a graph which exist loops or multiple edges. I want to create  it  .How should I do?  Thanks in advance.

my code like this

with(GraphTheory):
G:=Graph({{1,2},{1,5},{2,5},{2,3},{5,4},{3,4},{4,6}}):
G:=Graph({{1,1},{1,2},{1,5},{2,5},{2,3},{5,4},{3,4},{4,6}}):DrawGraph(G,style=spring);
G2:=Graph({{1,2}}):
DrawGraph(G2);
G3:=Graph({{1,2},{1,2}}):
DrawGraph(G3);

 

How I can get integral by part.

I want to calculate these integral.

Thank you

integral_part.pdf

 

How I can take Laplace Transform from equation.

Thanks

LAPLACE

Right now I am going through Bishop's ML book and as a part of the first exercise I need to define a polynomial that goes like this.

y(x,w) = w_0 + w_1 * x + w_2 * x^2 ... + w_m * x^m = sum (k=0 to m) w_k * x^k

Here is how I've written it out in Maple.

f := proc (x, w) options operator, arrow; sum(w[k]*x^k, k = 0 .. nops(w)) end proc

Sorry for the raw code, Maple Math won't accept the code I've written as a valid Maple expression for some reason. When I try to use this I get an error that says too many levels of recursion.

f(2, [a, b, c]);
Error, (in limit/mrv/limsimpl) too many levels of recursion

Where am I going wrong here?
 

Please look at this codes!!!

i cant understand the idea of how maple works with parameters...

Problem.JPG

if u watch it exactly u can see that first maple understands that diff(a__1,t) is equall 1; but anfter that it couldnt load the value 1.
why?

what is hapening?

what can i do for this problem. its not the main code. i just send u an example of what  i want and what maple does. plz help me. tnx 

Hi,

When multiple request to DocumentTools:-Tabulate(...) are enclosed in the same group of commands (which typically happens when they are within a procedure), only the last one is displayed.
Is it possible to overcome this behaviour?

Thanks in advance

Hello, everyone: I have a question of drawing graph。
restart:
with(GraphTheory):
with(SpecialGraphs):
H := HypercubeGraph(3):
DrawGraph(H,
style = spring);


How  do I change  the vertex style   to polygon without line.
the aim graph  like figure below:

Thank you very much!

 

Greeting for all 

 , How to plot gyroid surface by Maple where its equation is 

                            

Amr

I have the following ODE perturbation problem which I want maple to solve for me:

q'(\tau)=f(p(eps*\tau)+eps*q(\tau),r(eps*\tau)+s(\tau))-f(p(eps*\tau,r(eps*\tau)+s(\tau))-f(p(eps*\tau),r(eps*\tau))

 

where q(\tau)=q_0(\tau)+eps*q_1(\tau)

p(eps*\tau)=p_0(eps*\tau)+eps*p_1(eps*\tau)

s(\tau)=s_0(\tau)+eps*s_1(\tau)

r(eps*\tau)=r_0(eps*\tau)+eps*r_1(eps*\tau)

I want maple to expand every function that depends on eps in its arguments by a Taylor series around eps=0, i.e h(eps)=h(0)+eps*h'(0)

and also expand the difference above the fs with an eps-expansion around eps=0.

I did all this manually now I want to check if my calculations are correct, eventaully I want to equate same powers of eps of the RHS and LHS of the first ODE I wrote above.

 

Then how to use maple for this?

Thnaks.

 

Does there exist a Maple command that on its own calculates the residual standard error of two regression lists? 

Given the following functions, graph them and identify relative and absolute extrema (if any).

f(x)=3x^3-2x^2+5x-7     [-3,6]

How I can do ?

Thank you.

 

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and q = {`u__m,n`(t), `v__m,n`(t), `w__m,n`(t)}^T.

\where the elements of the vector,q_i are the time-dependent generalized coordinates.

L_Maple
 

U = (1/2)*(int(int(int(E*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x))+v(x, y, t)*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y))))*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x)))/(-nu^2+1)+E*(`∂`(nu(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y))+v(x, y, t)*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x))))*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y)))/(-nu^2+1)+E*(`∂`(u(x, y, t))/`∂`(y)+`∂`(v(x, y, t))/`∂`(x)+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w(x, y, t))/`∂`(y))+`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y))+`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y))-2*z*(diff(w(x, y, t), x, y)))^2/(2*(1+nu))+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), y, y)-(diff(w(x, y, t), x, x)))^2/(2*(1+nu))+E*l^2*(diff(v(x, y, t), y, y)-(diff(u(x, y, t), x, x)))^2/(8*(1+nu))+E*l^2*(diff(v(x, y, t), x, y)-(diff(u(x, y, t), y, y)))^2/(8*(1+nu)), z = -(1/2)*h .. (1/2)*h), y = 0 .. b), x = 0 .. a))

U = (1/2)*(int(int((1/12)*(-E*(-v(x, y, t)*(diff(diff(w(x, y, t), y), y))-(diff(diff(w(x, y, t), x), x)))*(diff(diff(w(x, y, t), x), x))/(-nu^2+1)-E*(-v(x, y, t)*(diff(diff(w(x, y, t), x), x))-(diff(diff(w(x, y, t), y), y)))*(diff(diff(w(x, y, t), y), y))/(-nu^2+1)+4*E*(diff(diff(w(x, y, t), x), y))^2/(2+2*nu))*h^3+E*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2+v(x, y, t)*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2))*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2)*h/(-nu^2+1)+E*(`∂`(nu(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2+v(x, y, t)*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2))*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2)*h/(-nu^2+1)+E*(`∂`(u(x, y, t))/`∂`(y)+`∂`(v(x, y, t))/`∂`(x)+`∂`(w(x, y, t))^2/(`∂`(x)*`∂`(y))+2*`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y)))^2*h/(2+2*nu)+2*E*l^2*(diff(diff(w(x, y, t), x), y))^2*h/(1+nu)+E*l^2*(diff(diff(w(x, y, t), y), y)-(diff(diff(w(x, y, t), x), x)))^2*h/(2+2*nu)+E*l^2*(diff(diff(v(x, y, t), y), y)-(diff(diff(u(x, y, t), x), x)))^2*h/(8+8*nu)+E*l^2*(diff(diff(v(x, y, t), x), y)-(diff(diff(u(x, y, t), y), y)))^2*h/(8+8*nu), y = 0 .. b), x = 0 .. a))

(1)

T = rho*h*(int(int((`∂`(u(x, y, t))/`∂`(t))^2+(`∂`(v(x, y, t))/`∂`(t))^2+(`∂`(w(x, y, t))/`∂`(t))^2, y = 0 .. b), x = 0 .. a))

T = rho*h*(int(int(`∂`(u(x, y, t))^2/`∂`(t)^2+`∂`(v(x, y, t))^2/`∂`(t)^2+`∂`(w(x, y, t))^2/`∂`(t)^2, y = 0 .. b), x = 0 .. a))

(2)

F = (1/2)*c*(int(int((`∂`(u(x, y, t))/`∂`(t))^2+(`∂`(v(x, y, t))/`∂`(t))^2+(`∂`(w(x, y, t))/`∂`(t))^2, y = 0 .. b), x = 0 .. a))

F = (1/2)*c*(int(int(`∂`(u(x, y, t))^2/`∂`(t)^2+`∂`(v(x, y, t))^2/`∂`(t)^2+`∂`(w(x, y, t))^2/`∂`(t)^2, y = 0 .. b), x = 0 .. a))

(3)

W = int(int(w(x, y, t)*f__1(x, y, t)*cos(omega*t), y = 0 .. b), x = 0 .. a)

W = int(int(w(x, y, z)*f__1(x, y, z)*cos(omega*t), y = 0 .. b), x = 0 .. a)

(4)

u(x, y, t) = sum(sum(`u__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

u(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(5)

v(x, y, t) = sum(sum(`v__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

v(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(6)

w(x, y, t) = sum(sum(`w__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

w(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(7)

diff(`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), t)-`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(F(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`) = `∂`(W(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), j = 1, () .. (), N

(D(`∂`))(T(x, y, t))*(diff(T(x, y, t), t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)-`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+2*`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(F(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`) = `∂`(W(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), j = 1, () .. (), N

(8)

NULL


 

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