Advanced Search

Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016
View unanswered posts
Maple 2016 Questions and Posts Feed

How to handle tolerance with eval...

Asked by: abdulganiy 140
eval incomplete-question
May 19 2023
0  4

I tried running the following codes but got error

restart;
Digits := 30:

f1 := proc(n)
    lamda * y1[n] + (y2[n])^2;
end proc:

f2 := proc(n)
    -y2[n];
end proc:

F1 := proc(n)
    lamda * f1(n) + 2 * f2(n) * y2[n];
end proc:

F2 := proc(n)
    -f2(n);
end proc:


e1 := y1[n+2] = (53/485) * y1[n] - (6/485) * F1(n+2) * h^2 + (6/485) * f1(n) * h +
                     (128/485) * f1(n+1/2) * h + (384/485) * f1(n+3/2) * h +
                     (432/485) * f1(n+1) * h + (20/97) * f1(n+2) * h +
                     (432/485) * y1[n+1] + (512/485) * y1[n+1/2] - (512/485) * y1[n+3/2]:

e2 := h^2 * F1(n+1/2) = -(9/970) * F1(n+2) * h^2 + (503/1940) * f1(n) * h -
                           (9412/1455) * f1(n+1/2) * h - (682/485) * f1(n+3/2) * h -
                           (4041/485) * f1(n+1) * h + (83/1164) * f1(n+2) * h +
                           (3878/1455) * y1[n] + (9054/485) * y1[n+1] -
                           (14166/485) * y1[n+1/2] + (11458/1455) * y1[n+3/2]:

e3 := h^2 * F1(n+1) = -(28/4365) * F1(n+2) * h^2 + (541/8730) * f1(n) * h +
                         (25072/13095) * f1(n+1/2) * h - (5968/4365) * f1(n+3/2) * h +
                         (224/485) * f1(n+1) * h + (269/5238) * f1(n+2) * h +
                         (7532/13095) * y1[n] - (9476/485) * y1[n+1] +
                         (4864/485) * y1[n+1/2] + (116992/13095) * y1[n+3/2]:

e4 := h^2 * F1(n+3/2) = -(31/970) * F1(n+2) * h^2 + (671/5820) * f1(n) * h +
                           (3902/1455) * f1(n+1/2) * h + (12676/1455) * f1(n+3/2) * h +
                           (5481/485) * f1(n+1) * h + (329/1164) * f1(n+2) * h +
                           (1502/1455) * y1[n] + (9846/485) * y1[n+1] +
                           (5526/485) * y1[n+1/2] - (47618/1455) * y1[n+3/2]:

e5 := y2[n+2] = (53/485) * y2[n] - (6/485) * F2(n+2) * h^2 + (6/485) * f2(n) * h +
                     (128/485) * f2(n+1/2) * h + (384/485) * f2(n+3/2) * h +
                     (432/485) * f2(n+1) * h + (20/97) * f2(n+2) * h +
                     (432/485) * y2[n+1] + (512/485) * y2[n+1/2] - (512/485) * y2[n+3/2]:

e6 := h^2 * F2(n+1/2) = -(9/970) * F2(n+2) * h^2 + (503/1940) * f2(n) * h -
                           (9412/1455) * f2(n+1/2) * h - (682/485) * f2(n+3/2) * h -
                           (4041/485) * f2(n+1) * h + (83/1164) * f2(n+2) * h +
                           (3878/1455) * y2[n] + (9054/485) * y2[n+1] -
                           (14166/485) * y2[n+1/2] + (11458/1455) * y2[n+3/2]:

e7 := h^2 * F2(n+1) = -(28/4365) * F2(n+2) * h^2 + (541/8730) * f2(n) * h +
                         (25072/13095) * f2(n+1/2) * h - (5968/4365) * f2(n+3/2) * h +
                         (224/485) * f2(n+1) * h + (269/5238) * f2(n+2) * h +
                         (7532/13095) * y2[n] - (9476/485) * y2[n+1] +
                         (4864/485) * y2[n+1/2] + (116992/13095) * y2[n+3/2]:

e8 := h^2 * F2(n+3/2) = -(31/970) * F2(n+2) * h^2 + (671/5820) * f2(n) * h +
                           (3902/1455) * f2(n+1/2) * h + (12676/1455) * f2(n+3/2) * h +
                           (5481/485) * f2(n+1) * h + (329/1164) * f2(n+2) * h +
                           (1502/1455) * y2[n] + (9846/485) * y2[n+1] +
                           (5526/485) * y2[n+1/2] - (47618/1455) * y2[n+3/2]:

Digits := 30: lamda := 10000:
h := 0.1:
N := solve(h*p = 10/4, p):
n := 0:
exy1 := [seq](eval(-exp(-2*i/2)/(lamda+2)), i = h .. N, h):
exy2 := [seq](eval(exp(-i/2)), i = h .. N, h):

iny1 := 1:
iny2 := 1:

c := 1:
vars := y1[n+1/2], y1[n+1], y1[n+3/2], y1[n+2], y2[n+1/2], y2[n+1], y2[n+3/2], y2[n+2]:

printf("%6s%15s%15s%15s%15s%10s%10s\n", 
    "h", "numy1", "numy2", 
    "exy1", "exy2", 
    "erry1", "erry2");

tolerance := 1e-6:
st := time():
for k from 1 to N do

    res := eval(<vars>, fsolve(eval({e||(1..8)}, [y1[n]=iny1, y2[n]=iny2]), {vars}), tolerance = tolerance):

    for i from 1 to 4 do
        printf("%6.5f%15.10f%15.10f%15.8g%15.10g%10.3g%10.3g\n", 
        h*c, res[i], res[i+4], 
        exy1[c], exy2[c], 
        abs(res[i]-exy1[c]), abs(res[i+4]-exy2[c])):

        c := c+1:
    end do:
    iny1 := res[4]:
    iny2 := res[8]:
end do:
v := time() - st:
 

3D plot of robot and Wankel engine using a single...

by: Mahardika Mathematics 30 Maple 2016
implicit plotting
April 17 2023
1  2

TODAY I GOT AN INSPIRATION TO CREATE 3D GRAPH EQUATION OF WALKING ROBOT (ED-209) IN CARTESIAN SPACE USING ONLY WITH SINGLE IMPLICIT EQUATION.

ENJOY...

 

How to Create Graph Equation of Wankel Engine on Cartesian Plane using Single Implicit Function run by Maple Software

Enjoy...

 

Where the error in the following code?...

Asked by: khalil20232023 15
homework differential-equations duplicate-question
April 15 2023
1  0

alpha1 := .8; alpha2 := .6; eq1 := fracdiff(x(t), t, alpha1)-t^2*x(t)+y(t)-2*t = 0; eq2 := fracdiff(y(t), t, alpha2)-2*z(t)+2*(t+1) = 0; eq3 := z(t)-y(t)-2*t*x(t)+t^4-t-1 = 0; N := 4; x0 := 0; y0 := 0; z0 := 1; XT1 := D[xt](eq1); XT2 := D[xt](eq2); XT3 := D[xt](eq3); XT1[0] := x0; XT2[0] := y0; XT3[0] := z0; for n to N do XT1[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT1))), t); XT2[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT2))), t); XT3[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT3))), t) end do; xseries := add(XT1[n](t)*t^(n*alpha1)/factorial(n*alpha1), n = 0 .. N); yseries := add(XT2[n](t)*t^(n*alpha2)/factorial(n*alpha2), n = 0 .. N); zseries := add(XT3[n](t)*t^(n*alpha2)/factorial(n*alpha2), n = 0 .. N); x_sol := unapply(xseries, t); y_sol := unapply(yseries, t); z_sol := unapply(zseries, t); print(x_sol); print(y_sol); print(z_sol)

proc (t) options operator, arrow; 1.000000000+1.119174954*XT3[1](t)*t^.6+.9076036841*XT3[2](t)*t^1.2+.5964840410*XT3[3](t)*t^1.8+.3354346720*XT3[4](t)*t^2.4 end proc

 (1)

``

Download Ex2_FDAEs.mw

I can not explore the error when I run this code b...

Asked by: khalil20232023 15
homework differential-equations fractional-derivative
April 10 2023
1  1

restart;

Frac_C := proc (expr, a, t, alpha) local ig, m, tau;

m := ceil(alpha);

ig := (t-tau)^(m-alpha-1)*(diff(eval(expr, t = tau), tau$m));

`assuming`([(int(ig, tau = a .. t))/GAMMA(m-alpha)], [a < t]);

end proc;
r := .5;

k := .7;

eq1 := Frac_C(x, 0, t, r)-y(t) = 0;

eq2 := Frac_C(y, 0, t, k)-x(t)-2*t = 0;

eq3 := x(0)-y(1) = 0;

eq4 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x), x = 1)) = 0;

eq5 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x, x), x = 1)) = 0;

eq6 := eval(diff(y(x), x), x = 0)-x(1)-2 = 0;

eq7 := y(0) = 0;

N := 5;

x[c] := [seq(a[i], i = 0 .. N)];

y[c] := [seq(b[i], i = 0 .. N)];

for n to N do

subs([seq(x(i) = x[c][i], i = 0 .. n), seq(y(i) = y[c][i], i = 0 .. n)], {eq1, eq2, eq3, eq4, eq5, eq6, eq7});
soln := solve({eq3, eq4, eq5, eq6, eq7, seq(coeff(lhs(eq), t, j) = 0, eq in {eq1, eq2})}, {a[n+1], b[n+1]});

x[c][n+1] := eval(a[n+1], soln);

y[c][n+1] := eval(b[n+1], soln);

end do;

x[s] := add(x[c][i]*t^(i-1), i = 1 .. N+1);

y[s] := add(y[c][i]*t^(i-1), i = 1 .. N+1);

x[s];

y[s];

plot of dna helix using as parametric surface

by: Mahardika Mathematics 30 Maple 2016
parametric plotting helix
April 09 2023
1  1

CREATING GRAPH EQUATION OF "DNA" IN CARTESIAN SPACE USING PARAMETRIC SURFACE EQUATION RUN ON MAPLE SOFTWARE

ENJOY...

 

Creating Graph Equation of Water Drop Wave in...

by: Mahardika Mathematics 30 Maple 2016
implicit plotting
April 03 2023
1  0

How to Create Graph Equation of Water Drop Wave in Cartesian Space using single Implicit Function only run by Maple Software

The Equation is:   z = - cos( (x2+y2)0.5 - a)  with paramater a is moving form 0 to 2pi 

Enjoy...

Plese Click link below to see full equation in Maple software

Water_Drop_Wave.mw

plots using only single implicit functions

by: Mahardika Mathematics 30 Maple 2016
animation implicit plotting
March 29 2023
1  5

Creating Graph Equation of An Apple in Cartesian Space using single Implicit Function only run by Maple software

Enjoy...

Please click the link below to see full equation on Maple file:

2._Apel_3D_A.mw

 

Creating Graph Equation of A Candle on Cartesian Plane using single Implicit Function only run by Maple software

Enjoy...

 

Today I'm very greatfull to have Inspiration to create Graph Equation of 3D Candle in Cartesian Space using single 3D Implicit Function only, run by Maple software.

Enjoy... 

 

Today I got an inspiration to create graph equation of "Petrol Truck" using only with Single Implicit Equation in Cartesian space run by Maple Software

Maple software is amazing...

Enjoy...

 

CREATING 3D GRAPH EQUATION OF BACTERIOPHAGE USING ONLY WITH SINGLE IMPLICIT EQAUTION IN CARTESIAN SPACE RUN BY MAPLE SOFTWARE

MAPLE SOFTWARE IS AMAZING...

ENJOY...

 

GRAPH EQUATION OF A FEATHER

AND THE EQUATION IS:

ENJOY...

I like this Equation and post it because it is so beautiful...

Click this link below to see full equation and download the Maple file: 

Bulu_Angsa_3.mw

 

GRAPH EQUATION OF "383" CREATED BY DHIMAS MAHARDIKA

ENJOY...

> 

with(plots):

DHIMAS MAHARDIKA EQUATION

> 

plots:-implicitplot(15-8.*cos(y)^(79/2)-32.*cos(y)^(37/2)+96.*cos(y)^(33/2)-96.*cos(y)^(29/2)+4.*cos(x)^(61/2)+4.*cos(x)^(31/2)-12.*cos(x)^(27/2)+12.*cos(x)^(23/2)+24.*cos(y)^29-48.*cos(y)^27+16.*cos(y)^8-64.*cos(y)^6+96.*cos(y)^4-4.*cos(x)^(19/2)-6.*cos(x)^19-4.*cos(x)^(57/2)+32.*cos(y)^(25/2)+24.*cos(y)^25+8.*cos(y)^(75/2)-cos(x)^38+cos(y)^50-64.*cos(y)^2+4.*cos(x)^2-6.*cos(x)^4+4.*cos(x)^6-cos(x)^8+12.*cos(x)^21-6.*cos(x)^23, x = -15 .. 15, y = -15 .. 15, numpoints = 50000, thickness = 4, colour = blue)

 
> 

NULL

Download 383.mw

How can I handle this error?...

Asked by: OLOWE RUTH 5
syntax differential-equations
March 22 2023
1  4

I'm trying to solve a system of differential equations and encountered this error: Error, (in fsolve) {f1[0], f1[1], f1[2], f1[3], f2[0], f2[1], f2[2], f2[3]} are in the equation, and are not solved for. How can this error be rectified?

Non zero Christoffel display ...

Asked by: albivaldmaple 20
tensor physics christoffel
March 08 2023
2  1

Hello everyone

I create a curved space ( with Physics) and create a metric tensor of 

a sphere . I see some Christoffel correcly . Is it possible to visualize all non zero Christoffel in one shot ?

Thank's a lot

Best Regards

restart; with(Physics)

Physics:-Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)

Physics:-Setup(spacetimeindices, dimension = 2, signature = "++")

[dimension = 2, signature = `+ +`, spacetimeindices = greek]

 (2)

Physics:-Coordinates(X)

{X}

 (3)

ds2 := Physics:-`^`(dx1, 2)+Physics:-`*`(Physics:-`^`(sin(x1), 2), Physics:-`^`(dx2, 2))

dx1^2+sin(x1)^2*dx2^2

 (4)

NULL

Physics:-Setup(metric = ds2)

[metric = {(1, 1) = 1, (2, 2) = sin(x1)^2}]

 (5)

NULL

NULL

g_[]

g[mu, nu] = (Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 2) = sin(x1)^2}, storage = triangular[upper], shape = [symmetric]))

 (6)

Physics:-Christoffel[`~k`, i, j]

Physics:-Christoffel[`~k`, i, j]

 (7)

Physics:-Christoffel[`~1`, 2, 2]

-sin(x1)*cos(x1)

 (8)

Physics:-Christoffel[`~2`, 1, 2]

cos(x1)/sin(x1)

 (9)

Physics:-Christoffel[`~1`, 1, 1]

0

 (10)

Download Approfondimento_1_-_Calcolo_Sfera_2D.mw

How I can solve these equations...

Asked by: NIMA112 10
solve fsolve
February 28 2023
1  0

how I can solve these equations?

Fung.mws

> 

 

> 

restart:
> 

with(LinearAlgebra):
> 

with(VectorCalculus):
> 

Q:=a_11*(E_r)^2+a_22*(E_theta)^2+a_33*(E_z)^2+2*a_12*E_r*E_theta+2*a_13*E_r*E_z+2*a_23*E_theta*E_z:
> 

psi:=0.5*c*(Q+0.5*Q^2):
> 

F:=matrix([[B*R/r,0,0],[0,r/R,0],[0,0,1/B]]):
> 

#b:=matrix([[B^2*R^2/r^2,0,0],[0,r^2/R^2,0],[0,0,1/B^2]]):
> 

b:=matrix([[B*(r^2-A)/r^2,0,0],[0,B*r^2/(r^2-A),0],[0,0,1/B^2]]):
> 

sigma_r:=-p+diff(psi,E_r)*b[1,1]:
> 

sigma_theta:=-p+diff(psi,E_theta)*b[2,2]:
> 

sigma_z:=-p+diff(psi,E_z)*b[3,3]:
> 

#H:=p_o+subs(r=r_o,diff(psi,E_r)*b[1,1]):
> 

H:=p_o+subs(r=sqrt(B*(R_o)^2+A),diff(psi,E_r)*b[1,1]):
> 

E_r:=0.5*(((B*r^2-B*A)/r^2)-1):
> 

E_theta:=0.5*((B*r^2/(r^2-A))-1):
> 

E_z:=0.5*((1/B^2)-1):
> 

H:
> 

p:=subs(r=sqrt(B*(R_o)^2+A),H):
> 

x0:=simplify((sigma_r-sigma_theta)/r):
> 

y0:=simplify(sigma_z*r):
> 

x1:=int(x0,r):
> 

y1:=2*Pi*int(y0,r):
> 

Digits:=50:
> 

p_i:=1.858e3:
> 

p_o:=0:
> 

R_i:=1:
> 

R_o:=10:
> 

a_11:=165.857:
> 

a_22:=47.028:
> 

a_33:=145.448:
> 

a_12:=46.747:
> 

a_13:=0.799:
> 

a_23:=14.587:
> 

c:=0.0004e6:
> 

F_a:=0:
> 

x2:=subs(r=sqrt(B*R^2+A),x1):
> 

y2:=subs(r=sqrt(B*R^2+A),y1):
> 

eq1:=subs(R=R_o,x2)-subs(R=R_i,x2):
> 

eq2:=subs(R=R_o,y2)-subs(R=R_i,y2):
> 

Eq1:=simplify(eq1):
> 

Eq2:=simplify(eq2):
> 

solve({Eq1=p_o-p_i,Eq2=F_a},{A,B});
> 

 

> 

%?

Download Fung.mws

Lorentz tansformation leaves Minkowski metric inv...

Asked by: albivaldmaple 20
February 04 2023
2  5

Hello everybody

I would like to check, with Spacetime Tensors computation , if  a transfomation is a Lorentz transformation , i.e that leavs Minkosky metric invariant 

For esample a boost  or axis rotation transformation

Some could help me ? ( Maple 2016)

Thank's a lot

Any comment, idea or innovation to calculate this ...

Asked by: mehdibgh 235
integration
January 14 2023
0  3

Any comment, idea or innovation to calculate this parametric integral?

Note M, II, JJ are arbitrary positive integers (0<M, II, JJ<11).

F must be a function of Pm at the final!

``

> 

restart
> 

M := 3:
> 

JJ := 5
> 

II := 5
> 

with(ArrayTools):
> 

W := RandomArray(II, JJ, M):
> 

V := ArrayTools:-RandomArray(II, JJ, M):
> 

w := add(add(add(W[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):
> 

v := add(add(add(V[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):
> 

L := add(add((LegendreP(i-1, x)*LegendreP(j-1, y))^2, i = 1 .. II), j = 1 .. JJ):
> 

H := 1+tanh(w-v)
> 

F := int(H*L, [y = -1 .. 1, x = -1 .. 1])

Warning,  computation interrupted

  
> 

``
> 

``

Download integralproblem.mw

Don't know where the error is from...

Asked by: kencom1 100
pde numeric pdsolve
January 08 2023
1  4

Good day everyone,

I have been having problems with a system of PDE solution using `numeric`.

It's giving me the error code "Error, (in pdsolve/numeric/par_hyp) input system is too far from a 'standard' form (see ?pdsolve,numeric for more detail)" and I have checked to the best of my ability for the error but could not see anything.

The code is attached below.

Please, anyone with useful information should help. Thanks

Numeric.mw

Solve a system of nonlinear algebraic equations...

Asked by: moh111 15
solve
October 30 2022
1  5

How can these eight equations q[0]...q[7] be solved for the eight unknowns a1[0]...a1[7] and with the lowest CPU time

11.mw

Transplots not working for PDE...

Asked by: kencom1 100
syntax transform plotting
October 23 2022
0  2

Good day everyone,

I am trying to rotate the plots of pde solution using transplot, but it is giving me errors. Anyone with better suggestions should help. The code is attached below. Thanks

Transplot_not_working.mw

1 2 3 4 5 6 7 Last Page 1 of 60