Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

Dear Users!

Hope everything going find with you. I want to generate sequence of Spline[i,p], p=1…M as given bellow

restart; M := 3;
for p while p <= M do
(x-x[i])*B[i, p-1]/(x[i+p]-x[i])+(x[i+p+1]-x)*B[i+1, p-1]/(x[i+p+1]-x[i+1]);
B[i, p] := collect(%, [`$`(B[i+s, 0], s = 0 .. M)]);
B[i+1, p] := eval(%, i = i+1)
end do;
for p while p <= M do
Spline[i, p] := B[i, p]
end do

The expression for Spline[i,1] and Spline[i,2] are fine but the expressions of Spline [i,p] p>2 is not in simplified form I got the its simplification like given bellow for Spline[i,3]

Spline[i, 3]:=(x-x[i])^3*B[i, 0]/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+1]-x[i]))+(((x-x[i])*(x-x[i]))*(x[i+2]-x)/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+2]-x[i+1]))+(x-x[i])*(x[i+3]-x)*(x-x[i+1])/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1]))+(x[i+4]-x)*(x-x[i+1])^2/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1])))*B[i+1, 0]+((x-x[i])*(x[i+3]-x)^2/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+(x[i+4]-x)*(x-x[i+1])*(x[i+3]-x)/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+((x[i+4]-x)*(x[i+4]-x))*(x-x[i+2])/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+3]-x[i+2])))*B[i+2, 0]+(x[i+4]-x)^3*B[i+3, 0]/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+4]-x[i+3]));

I am waiting for positive respone. Please take care and thanks in advance

Hi,

I want to solve this system of PDEs. Please let me know how I can solve it.

Kindly find both my code written in Maple and the image of the problem.

Best,

 

PDE.mw

Dear Users!
Hope everyone fine here. I tried (as given bellow) to find the solution of nonlinear system of PDEs via FDM. To solve system of nonlinear equations I used newton raphson method and for higher value of like Mx > 8 the matrix G and G1 (mentioned as red) take alot of time. Can anyone help me to reduce the computational time? Becuase I have to evealuate the solution for Mx = 50.


restart; Digits := 30; with(LinearAlgebra);
T := 1; L := 3; N := 30; Mx := 5; `&Delta;x` := L/(1.*Mx); `&Delta;t` := T/(1.*N);
for i from 0 while i <= Mx do
u[i, 0] := 0.; u[i, -1] := u[i, 1]; tau[i, 0] := 0.; theta[i, 0] := 0.; theta[i, -1] := theta[i, 1]
end do;
for n from 0 while n <= N do u[0, n] := 0.; u[Mx, n] := 0.; theta[0, n] := 1.; theta[Mx, n] := 0.
end do;
for n from 0 while n <= N-1 do
print("Simulation in proccess at time-level n", n+1);
for i while i <= Mx-1 do
Ru[i, n] := simplify((u[i+1, n+1]-u[i+1, n])/`&Delta;t`+(u[i+1, n+1]-2*u[i+1, n]+u[i+1, n-1])/`&Delta;t`^2-(u[i+1, n+1]-2*u[i, n+1]+u[i-1, n+1])/`&Delta;x`^2+25.*(u[i+1, n+1]+(u[i+1, n+1]-u[i+1, n])/`&Delta;t`)-1.5*(theta[i, n]+(theta[i, n+1]-theta[i, n])/`&Delta;t`));
`R&theta;`[i, n] := simplify((theta[i+1, n+1]-theta[i+1, n])/`&Delta;t`+(theta[i+1, n+1]-2*theta[i+1, n]+theta[i+1, n-1])/`&Delta;t`^2-(theta[i+1, n+1]-2*theta[i, n+1]+theta[i-1, n+1])/((15.)*`&Delta;x`^2)-((u[i, n+1]-u[i-1, n+1])/`&Delta;x`)^2/(3.)) end do;
for i while i <= Mx-1 do
`R&tau;`[i, n] := simplify(tau[i+1, n+1]+(tau[i+1, n+1]-tau[i+1, n])/`&Delta;t`-1.5^(-1/4)*(u[i+1, n+1]-u[i, n+1])/`&Delta;x`)
end do;
Sys := `<,>`(seq(Ru[i, n], i = 1 .. Mx-1), seq(`R&tau;`[i, n], i = 1 .. Mx-1), seq(`R&theta;`[i, n], i = 1 .. Mx-1));
V := `<,>`(seq(u[i, n+1], i = 1 .. Mx-1), seq(theta[i, n+1], i = 1 .. Mx-1), seq(tau[i, n+1], i = 2 .. Mx));
G := Matrix(3*(Mx-1), proc (i, j) options operator, arrow; diff(Sys[i], V[j]) end proc); G1 := MatrixInverse(G);
X[n, 0] := Vector(1 .. 3*(Mx-1), 1);
for k1 from 0 to r do
X[n, k1+1] := eval(V-G1 . Sys, Equate(V, X[n, k1]))
end do;
Sol[n] := Equate(V, X[n, r+1]); assign(op(Sol[n]));
if n > 0 then
U := eval(`<,>`(seq(u[i1, n+1], i1 = 1 .. Mx)-seq(u[i1, n], i1 = 1 .. Mx))); Noru[n+1] := Norm(%, 2); print("L[&infin;] norm of &tau;(x,y,t) at time level = ", %);
Theta := eval(`<,>`(seq(theta[i1, n+1], i1 = 0 .. Mx)-seq(theta[i1, n], i1 = 0 .. Mx))); `Nor&theta;`[n+1] := Norm(%, 2); print("L[&infin;] norm of &theta;(x,y,t) at time level = ", %) else print("n < 0")
end if end do

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

I just got a "new" graphics card, NVIDIA GT630, and was wondering whether the CUDA capabilities are accessible. But no luck:

CUDA:-Enable();

Error, (in CUDA:-Enable) CUDA not supported on the current system (see CUDA,supported_hardware for more information)

The CUDA help page with the example, when run, just shows a host of error messages.

I have OS X 10.11.6, the above mentioned GT630 card with claimed 384 CUDA cores and 2 GB of VRAM; NVIDIA WebDriver 346.03.15f16 for the card (i.e. latest for this OS) and NVIDIA CUDA driver 8.0.90 (again, latest for this OS as far as I can tell). My Maple is 2015.2. All this running on a MacPro 4,1.

I am not having great illusions about the performance I should get (this is not a state-of-the-art card today), but it seems to me this combination should be working with Maple 2015 and not throw an error, shouldn't it? Checking the system extensions: CUDA.kext is loaded and its dependencies are satisfied, so I don't see any problem there.

Am I missing something?

M.D.

I used dsolve to solve the Initial value problems numericaly.
When I set the parameter range=1..5*10^4 , it works and cost only about 200s cpu time.
But if I set range=1..2*10^5, it stop running ( cpu time stop) when the mserver memory reach about 1.5 G. (the memory record in the bottom-right of maple interface is about 700M .)

What is the reason please?  

Hi everyone! Currently I'm studying magnetism, and I was thinking that maybe seeing represented the helix movement of an atom with a vector v parallel to the Magnetic Field B subject to the Force of Lorentz and the Hysteresis cycle created in the magnetazation of a ferromagnetic material could help me understand it more. I tried to create the plots in Maple 2015 but I couldn't.. anyone can help me by creating those two plots?

Hi, 

I represent 3 thin parallel slices of colors red, green and blue; all have the same transparency equal to 0.5
For the default orientation of the display, the blue slice is on the forefront, the red one in the background and the green one in beween. Then the blue slice is "bluer" than green and  the green one "greener" than red (FIG 1)
If you rotate manually the figure in order to place the red slice in the forefront and the blue one in the background, you expect to have the red slice "redder" than the green one and the green one "greener" than the blue one (FIG 2)
This is not the case.

The order in which the slices appear in the PLOT3D command defines the foreground and the background, but these latter are not dynamically recalculated when the figure is rotated.
To recover the correct colors one must revert the order of the slices in PLOT3D (FIG 3)

Are we comdamned to change to change manually the order of the slices in PLOT3D or does it exist an option whixh avoids doing so?

Don't pay too much attention to the plots above for the foreground is strangely correct on figure 2 ???

restart

with(plottools):

alpha := Pi/18.:
a := 2*cos(alpha):
b := 2*sin(alpha):
e := 0.02:
p := [[0,0,0],[a,b,0],[a,b,1],[0,0,1]],
     [[0,e,0],[a,b+e,0],[a,b+e,1],[0,e,1]],
     [[0,0,0],[0,e,0],[0,e,1],[0,0,1]],
     [[a,b,0],[a,b+e,0],[a,b+e,1],[a,b,1]],
     [[0,0,0],[a,b,0],[a,b+e,0],[0,e,0]],
     [[0,0,1],[a,b,1],[a,b+e,1],[0,e,1]]

[[0, 0, 0], [1.969615506, .3472963554, 0], [1.969615506, .3472963554, 1], [0, 0, 1]], [[0, 0.2e-1, 0], [1.969615506, .3672963554, 0], [1.969615506, .3672963554, 1], [0, 0.2e-1, 1]], [[0, 0, 0], [0, 0.2e-1, 0], [0, 0.2e-1, 1], [0, 0, 1]], [[1.969615506, .3472963554, 0], [1.969615506, .3672963554, 0], [1.969615506, .3672963554, 1], [1.969615506, .3472963554, 1]], [[0, 0, 0], [1.969615506, .3472963554, 0], [1.969615506, .3672963554, 0], [0, 0.2e-1, 0]], [[0, 0, 1], [1.969615506, .3472963554, 1], [1.969615506, .3672963554, 1], [0, 0.2e-1, 1]]

(1)

f   := k -> transform((x, y, z) -> [x, y+k, z]):
col := k-> COLOR(RGB, op(ListTools:-Rotate([1, 0, 0], -k))):
t   := TRANSPARENCY(0.5):
PLOT3D(POLYGONS(p, t, col(0)), f(1)(POLYGONS(p, t, col(1))), f(2)(POLYGONS(p, t, col(2))), AXESLABELS(2, 3, 1))

 

PLOT3D(POLYGONS(p, t, col(0)), f(1)(POLYGONS(p, t, col(1))), f(2)(POLYGONS(p, t, col(2))), AXESLABELS(2, 3, 1))

 

PLOT3D(f(2)(POLYGONS(p, t, col(2))), f(1)(POLYGONS(p, t, col(1))), POLYGONS(p, t, col(0)), AXESLABELS(2, 3, 1))

 

 


 

Download Background_Foreground.mw

I find some book teach motion planning in topology 

but do it need to formulate the equations for the environments such as a map with obstacle in 2d or 3D?  the environment is quite complex, how can these equations be formulated?

 

Can old maple version saved .m files in window be readable in maple 2015 Linux version?

Hi!

There is a (relatively) known software code (written in C), called ." GKLS-generator" or "GKLS" to generate, according to certain user paramenters, optimization test functions. The code is available for free at the web

http://wwwinfo.deis.unical.it/%7Eyaro/GKLS.html

The download with the files of the GKLS is the following:  download

I would like to write this code in Maple. In the attached zip there is a PDF explaining how to build these functions. For now, I tried the follwoing Maple code GKLS_v4.mw

I think I'm doing something wrong, since the drawing generated by the attached Maple does not look much like the PDF in the attached zip (Fig. 1 of page 8).

Please, Can you help me with this?

Many thanks in advance for your comments.

 

 

Dear Users!

Hope you would be fine with everything. I want the simpliest for of the following expression in two step:

diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z))+u[delta]*lambda[1]*(diff(U(X, Y, Z, tau), tau, tau))/L[delta]+u[delta]*lambda[1]*(diff(U(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), X))/L[delta]+u[delta]*lambda[1]*U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, X))/L[delta]+u[delta]*lambda[1]*(diff(V(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), Y))/L[delta]+u[delta]*lambda[1]*V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, Y))/L[delta]+u[delta]*lambda[1]*(diff(W(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), Z))/L[delta]+u[delta]*lambda[1]*W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, Z))/L[delta];
Step 1:
diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z))+u[delta]*lambda[1]*(diff(diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z)), tau))/L[delta];
Step 2: (final form I need)
(1+(u[delta] lambda[1])/(L[delta]) (&PartialD;)/(&PartialD;tau)) ((&PartialD;)/(&PartialD;tau) U(X,Y,Z,tau)+U(X,Y,Z,tau) ((&PartialD;)/(&PartialD;X) U(X,Y,Z,tau))+V(X,Y,Z,tau) ((&PartialD;)/(&PartialD;Y) U(X,Y,Z,tau))+W(X,Y,Z,tau) ((&PartialD;)/(&PartialD;Z) U(X,Y,Z,tau)));
I'm waiting for your response.
Special request:
@acer @Carl Love @Kitonum @Preben Alsholm

Hi

I would like to use  the Liebniz notation that someone from the technical support posted here
Writing Derivatives at a Point Using Leibniz Notation
to display a formula that is not just a partial derivative but a more complex expression invoking partial derivatives. 
Typically an expression like this one:

2*(Diff(f(mu__1, mu__2), mu__1))^2*lambda__1^2-(Diff(f(mu__1, mu__2), mu__1))^2*mu__1^2+2*(Diff(f(mu__1, mu__2), mu__2))^2*lambda__2^2-(Diff(f(mu__1, mu__2), mu__2))^2*mu__2^2+2*(Diff(f(mu__1, mu__2), mu__1))*(Diff(f(mu__1, mu__2), mu__2))*lambda__1*lambda__2-2*(Diff(f(mu__1, mu__2), mu__1))*mu__1*(Diff(f(mu__1, mu__2), mu__2))*mu__2

Could anyone help me to do this?
Thanks in advance

(PS: I'm still using Maple 2015.2)

is there any library or tools to design index of Grassmannian and its k and n for Schubert use?

is there any library to relate poset with index of Grassmannian and its k and n for Schubert use

hello everyone,
   INGT.mw
 

L__d := 100:

L__b := 200:

L__c := L__d+(1/2)*L__b;

200

(1)

X := .3;

.3

(2)

Error, (in plot) procedure expected, as range contains no plotting variable

 

`&Delta;E__g` := 1.155*X+.37*X^2;

.3798

(3)

V__0 := .6*`&Delta;E__g`;

.22788

(4)

m__D := 0.67e-1*m[e];

0.67e-1*m[e]

(5)

m__B := (0.67e-1+0.83e-1*X)*m[e];

0.919e-1*m[e]

(6)

Sol := solve(2*cos(L__d*sqrt(E__x))+(m__D*sqrt((V__0-E__x)/E__x)/m__B-m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))-(m__D*sqrt((V__0-E__x)/E__x)/m__B+m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))*exp(-sqrt(V__0-E__x)*L__b) = 0, E__x);

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(7)

 

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(8)

E__1 := 0.1110897170e-2:

K__1 := sqrt(E__1);

0.3333012406e-1

(9)

K__2 := sqrt(V__0-E__1);

.4762027959

(10)

C := cosh((1/2)*K__2*L__b);

0.2399908351e21

(11)

beta := m__D*K__2/(m__B*K__1);

10.41631973

(12)

B := -beta*sinh((1/2)*K__2*L__b);

-0.2499821271e22

(13)

A := -B*sin(K__1*L__d)+C*cos(K__1*L__d);

-0.7112056933e21

(14)

h := proc (x) options operator, arrow; piecewise(x <= -L__c, A*exp(K__2*(x+L__c)), -L__c < x and x < -(1/2)*L__b, -B*sin(K__1*(x+(1/2)*L__b))+C*cos(K__1*(x+(1/2)*L__b)), abs(x) <= (1/2)*L__b, (1/2)*exp(K__2*x)+(1/2)*exp(-K__2*x), (1/2)*L__b < x and x < L__c, -B*sin(K__1*(x-(1/2)*L__b))+C*cos(K__1*(x-(1/2)*L__b)), L__c <= x, A*exp(K__2*(x-L__c))) end proc:

'h(x)' = h(x);

h(x) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))

(15)

L__y := 200:

L__z := 200:

P := proc (x, y, z) options operator, arrow; h(x)*cos(Pi*y/L__y)*cos(Pi*z/L__z) end proc:

'Psi(x, y, z)' = P(x, y, z);

Psi(x, y, z) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))*cos((1/200)*Pi*y)*cos((1/200)*Pi*z)

(16)

INGT := proc (x__i) `assuming`([evalf(int(int(int(P(x, y, z)^2*exp(-lambda*sqrt((x-x__i)^2+y^2+z^2)), x = -infinity .. infinity), y = -L__y .. L__y), z = -L__z .. L__z))], [0 < lambda]) end proc

evalf(INGT(2))

``

Warning,  computation interrupted

 

``


 

Download INGT.mw
 

L__d := 100:

L__b := 200:

L__c := L__d+(1/2)*L__b;

200

(1)

X := .3;

.3

(2)

Error, (in plot) procedure expected, as range contains no plotting variable

 

`&Delta;E__g` := 1.155*X+.37*X^2;

.3798

(3)

V__0 := .6*`&Delta;E__g`;

.22788

(4)

m__D := 0.67e-1*m[e];

0.67e-1*m[e]

(5)

m__B := (0.67e-1+0.83e-1*X)*m[e];

0.919e-1*m[e]

(6)

Sol := solve(2*cos(L__d*sqrt(E__x))+(m__D*sqrt((V__0-E__x)/E__x)/m__B-m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))-(m__D*sqrt((V__0-E__x)/E__x)/m__B+m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))*exp(-sqrt(V__0-E__x)*L__b) = 0, E__x);

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(7)

 

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(8)

E__1 := 0.1110897170e-2:

K__1 := sqrt(E__1);

0.3333012406e-1

(9)

K__2 := sqrt(V__0-E__1);

.4762027959

(10)

C := cosh((1/2)*K__2*L__b);

0.2399908351e21

(11)

beta := m__D*K__2/(m__B*K__1);

10.41631973

(12)

B := -beta*sinh((1/2)*K__2*L__b);

-0.2499821271e22

(13)

A := -B*sin(K__1*L__d)+C*cos(K__1*L__d);

-0.7112056933e21

(14)

h := proc (x) options operator, arrow; piecewise(x <= -L__c, A*exp(K__2*(x+L__c)), -L__c < x and x < -(1/2)*L__b, -B*sin(K__1*(x+(1/2)*L__b))+C*cos(K__1*(x+(1/2)*L__b)), abs(x) <= (1/2)*L__b, (1/2)*exp(K__2*x)+(1/2)*exp(-K__2*x), (1/2)*L__b < x and x < L__c, -B*sin(K__1*(x-(1/2)*L__b))+C*cos(K__1*(x-(1/2)*L__b)), L__c <= x, A*exp(K__2*(x-L__c))) end proc:

'h(x)' = h(x);

h(x) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))

(15)

L__y := 200:

L__z := 200:

P := proc (x, y, z) options operator, arrow; h(x)*cos(Pi*y/L__y)*cos(Pi*z/L__z) end proc:

'Psi(x, y, z)' = P(x, y, z);

Psi(x, y, z) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))*cos((1/200)*Pi*y)*cos((1/200)*Pi*z)

(16)

INGT := proc (x__i) `assuming`([evalf(int(int(int(P(x, y, z)^2*exp(-lambda*sqrt((x-x__i)^2+y^2+z^2)), x = -infinity .. infinity), y = -L__y .. L__y), z = -L__z .. L__z))], [0 < lambda]) end proc

evalf(INGT(2))

``

Warning,  computation interrupted

 

``


 

Download INGT.mw

 

I'm trying to calculate a triple integral complicated by a procedure that changes each time a variable xi, while the program takes a lot of time and it gives me the message "Warning, computation interrupted". If anyone can help me I will be very happy

Dear Users!

Hoped everyone fine here. I have three main questions regarding the maple code given bellow:

restart; with(LinearAlgebra); with(plots);

alpha := 1; beta := 1; theta := 1/2;

UU := sinh(x)*sinh(y)*sinh(z)*exp(-1.*t);

NN := 3; L := 0; R := 1; T := 1; N := NN; Mx := NN; My := NN; Mz := NN; `&Delta;x` := (R-L)/Mx; `&Delta;y` := (R-L)/My; `&Delta;z` := (R-L)/Mz; `&Delta;t` := (R-L)/N;

kappa[1] := 1; kappa[2] := 2/x^2; kappa[3] := 1/x^2; kappa[X] := x^2+y^2+z^2+1; kappa[Y] := x^2+y^2+z^2+1; kappa[Z] := x^2+y^2+z^2+1; kappa[4] := 0; NL := 3;

ics := [seq(seq(seq([u[i, j, k, 0] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0]), u[i, j, k, -1] = eval(u[i, j, k, 1]-2*`&Delta;t`*(eval(diff(UU, t), t = 0)), [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0])][], i = 0 .. Mx), j = 0 .. My), k = 0 .. Mz)];

bcs := [seq(seq(seq([u[0, j, k, n] = eval(UU, [x = 0, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[Mx, j, k, n] = eval(UU, [x = L, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`])][], j = 0 .. My), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, 0, k, n] = eval(UU, [x = i*`&Delta;x`, y = 0, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[i, My, k, n] = eval(UU, [x = i*`&Delta;x`, y = L, z = k*`&Delta;z`, t = n*`&Delta;t`])][], i = 1 .. Mx-1), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, j, 0, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = 0, t = n*`&Delta;t`]), u[i, j, Mz, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = L, t = n*`&Delta;t`])][], i = 1 .. Mx-1), j = 1 .. My-1), n = 1 .. N)];
Sol := {u[1, 1, 1, 1] = 0.2366497936e-1, u[1, 1, 1, 2] = 0.7589975856e-2, u[1, 1, 1, 3] = 0.6029906475e-3, u[1, 1, 2, 1] = 0.3778786317e-1, u[1, 1, 2, 2] = 0.7126415819e-2, u[1, 1, 2, 3] = -0.1197885714e-2, u[1, 2, 1, 1] = 0.3778786315e-1, u[1, 2, 1, 2] = 0.7126415820e-2, u[1, 2, 1, 3] = -0.1197885718e-2, u[1, 2, 2, 1] = 0.6038763054e-1, u[1, 2, 2, 2] = 0.4264591907e-2, u[1, 2, 2, 3] = -0.3509477851e-2, u[2, 1, 1, 1] = 0.3171958616e-1, u[2, 1, 1, 2] = -0.1327161715e-1, u[2, 1, 1, 3] = -0.4628647419e-2, u[2, 1, 2, 1] = 0.4979852397e-1, u[2, 1, 2, 2] = -0.3060811899e-1, u[2, 1, 2, 3] = -0.344914876e-4, u[2, 2, 1, 1] = 0.4979852397e-1, u[2, 2, 1, 2] = -0.3060811898e-1, u[2, 2, 1, 3] = -0.3449150010e-4, u[2, 2, 2, 1] = 0.7882396741e-1, u[2, 2, 2, 2] = -0.6192340018e-1, u[2, 2, 2, 3] = 0.1156615222e-1}

Using set of points given in ics, bcs and Sol

1. I want to contruct a vector at any time level (by fixing fourth suffix like u[i,j,k,n]) for i = 0..Mx,j=0..My,k=0..Mz and then find its L2 and L[infinity] norms.

2. Next I want contruct a vector by fixing two suffixes like u[i,j,k,n]) for i = 0..Mx,j=0..My and plot a surface in 3D

3. Finally I want to construct a vector by fixing three suffixes like u[i,j,k,n]) for i = 0..Mx, and plot a curve in 2D.

I'm waiting for your positive respone. I shall be very thankfull to you in advance.

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

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