Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

How can i plot a probability function such as cos(x-y)*cos(y-z)*cos^3(x-2z)=0.6 where

x=0..5, y=0..x, z=0..y.

please guide me.

i have a probability function f(x,y,z)=x^3*y*z and constraint on its ranges x<y , y<z. how can i plot it fot f(x,y,z)=0.5

Hi

Im going to solve mixing layer boundary layer equation in maple but Its this error: "Error, (in Shoot:-shoot) invalid boundary conditions, must be given at one point"

please help me. thank you.

> restart;
> alias(U = u(x, y), V = v(x, y)); PDE := {diff(U, x)+diff(V, y) = 0, U*(diff(U, x))+V*(diff(U, y))-nu*(diff(U, `$`(y, 2))) = 0};
print(`output redirected...`); # input placeholder
    // d   \   / d   \        / d   \     / d   \      / d  / d   \\    \ 
   { |--- U| + |--- V| = 0, U |--- U| + V |--- U| - nu |--- |--- U|| = 0 }
    \\ dx  /   \ dy  /        \ dx  /     \ dy  /      \ dy \ dy  //    / 
> simsubs := eta(x, y) = y*sqrt((1/2)*u[0]/(nu*x));
print(`output redirected...`); # input placeholder
                                                  (1/2)
                                 1    (1/2) /u[0]\     
                     eta(x, y) = - y 2      |----|     
                                 2          \nu x/     
> stream := psi(x, y) = sqrt(2*nu*x*u[0])*f(eta(x, y));
print(`output redirected...`); # input placeholder
                           (1/2)            (1/2)             
              psi(x, y) = 2      (nu x u[0])      f(eta(x, y))
> Usubs := U = diff(rhs(stream), y);
print(`output redirected...`); # input placeholder
              (1/2)            (1/2)                 / d           \
         U = 2      (nu x u[0])      D(f)(eta(x, y)) |--- eta(x, y)|
                                                     \ dy          /
> Vsubs := V = -(diff(rhs(stream), x));
print(`output redirected...`); # input placeholder
               (1/2)                     
              2      f(eta(x, y)) nu u[0]
        V = - ---------------------------
                               (1/2)     
                  2 (nu x u[0])          

              (1/2)            (1/2)                 / d           \
           - 2      (nu x u[0])      D(f)(eta(x, y)) |--- eta(x, y)|
                                                     \ dx          /
> ODE := simplify(subs(Usubs, Vsubs, simsubs, PDE));
print(`output redirected...`); # input placeholder
 /                             /      /           /                 (1/2)\  /    
 |                  1          |    2 |           |1    (1/2) /u[0]\     |  |1   
 |0 = 0, - ------------------- |u[0]  |@@(D, 2)(f)|- y 2      |----|     | f|- y 
<                        (1/2) \      \           \2          \nu x/     /  \2   
 |               2 /u[0]\                                                        
 |         2 nu x  |----|                                                        
 \                 \nu x/                                                        

               (1/2)\          (1/2)  
   (1/2) /u[0]\     |    /u[0]\       
  2      |----|     | nu |----|      x
         \nu x/     /    \nu x/       

                                 /                 (1/2)\\\    \ 
                (1/2)            |1    (1/2) /u[0]\     |||    | 
   + (nu x u[0])      @@(D, 3)(f)|- y 2      |----|     ||| = 0| 
                                 \2          \nu x/     ///     >
                                                               | 
                                                               | 
                                                               / 
> simsubs2 := solve(subs(eta(x, y) = eta, simsubs), {y});
print(`output redirected...`); # input placeholder
                              /         (1/2) \ 
                              |    eta 2      | 
                              |y = -----------| 
                             <           (1/2) >
                              |    /u[0]\     | 
                              |    |----|     | 
                              \    \nu x/     / 
> ODE := simplify(subs(simsubs2, ODE), symbolic);
print(`output redirected...`); # input placeholder
      /             2                                                 \ 
      |         u[0]  (@@(D, 2)(f)(eta) f(eta) + @@(D, 3)(f)(eta))    | 
     < 0 = 0, - -------------------------------------------------- = 0 >
      |                                2 x                            | 
      \                                                               / 

> shootlib := "C:\\Users/abbas/Desktop/maple9/"; libname := shootlib, libname; with(Shoot);
print(`output redirected...`); # input placeholder
                                   [shoot]
> FNS := {f(eta), g(eta), h(eta)};
> ODE := {diff(f(eta), eta) = g(eta), diff(g(eta), eta) = h(eta), diff(h(eta), eta) = -f(eta)*h(eta)};
print(`output redirected...`); # input placeholder
 /  d                      d                      d                          \ 
{ ----- f(eta) = g(eta), ----- g(eta) = h(eta), ----- h(eta) = -f(eta) h(eta) }
 \ deta                   deta                   deta                        / 
> IC := {f(0) = 0, g(0) = 0, h(0) = beta};
print(`output redirected...`); # input placeholder
                      {f(0) = 0, g(0) = 0, h(0) = beta}
> BC := {g(-10.) = 0, g(10.) = 1, limit(eta-f(eta), eta = 10) = 0};
print(`output redirected...`); # input placeholder
                  {10 - f(10) = 0, g(-10.) = 0, g(10.) = 1}
> infolevel[shoot] := 1;
print(`output redirected...`); # input placeholder
                                      1
> S := shoot(ODE, IC, BC, FNS, beta = 0, abserr = 0.5e-6, output = listprocedure, method = taylorseries);
%;
Error, (in Shoot:-shoot) invalid boundary conditions, must be given at one point
 

Hi, all i am unable to plot the graphs ,can any one help me to overcome the error in plotting the graphs.I am using the maple 13. I am attaching the codes

restart:
with(plots):
with(IntegrationTools):
d1:=0.2:L1:=0.2:L2:=0.2:B1:=0.7:B:=1:beta:=0.01:
d2:=0.6:m:=0.1:k:=0.1: 

h:=z->piecewise( z<=d1,    1,
                z<=d1+L1,   1-(gamma1/(2))*(1 + cos(2*(Pi/L1)*(z-d1-L1/2))), 
                z<=B1-L2/2,  1 ,          
                z<=B1,  1-(gamma2/(2))*(1 + cos(2*(Pi/L2)*(z - B1))),
                z<=B1+L2/2,  1-(gamma2/(2))*(1 + cos(2*(Pi/L2)*(z - B1))),
                 z<=B,    1):
                
A:=(-m^2/4)-(1/(4*k)):
S1:=(h(z)^2)/(4*A)-ln(A*h(z)^2+1)*(1+h(z)^2)/(4*A):
b1:=evalf((1/S1)):               
c1:=evalf(Int(b1,z=0..1)):

plot([seq(eval(c1,gamma2=j),j in[0,0.02,0.06])],gamma1=0.02..0.1,legend = [gamma2 = 0.0, gamma2 = 0.02,gamma2 =0.04],linestyle = [solid,dash,dot],color = [black, black,black],axes=boxed); 
 

wave2.mw

 

Hellow!

 

I'm use Maple 13 (Linux)

I want save the value of u(x,t) at output file. This function is solution of PDE.

 

Can I get one file to each time value??

 

Ths

 

 

Hi Maple experts and others,

We want to make a graph with 6 vertical lines.  One end of every vertical line will be on the x axis.  The other end of the vertical lines will be on integers of data points.

 


 

3+2

5

(1)

ab := Vector[row](6); cd := Vector[row](6)

ab := Vector[row](6, {(1) = 5, (2) = 8, (3) = 11, (4) = 14, (5) = 17, (6) = 20})

 

cd := Vector[row](6, {(1) = 1, (2) = 2, (3) = 3, (4) = 4, (5) = 5, (6) = 6})

(2)

for count to 6 do ab[count] := 3*count+2; cd[count] := count end do;

5

 

1

 

8

 

2

 

11

 

3

 

14

 

4

 

17

 

5

 

20

 

6

(3)

ab

Vector[row]([5, 8, 11, 14, 17, 20])

(4)

cd

Vector[row]([1, 2, 3, 4, 5, 6])

(5)

``


 

Download a_try.mw

Please assist us.

Regards,

Matt

 

Hellow,I use maple 13 (linux)

 

How can I get a output data file solution of my ODE? For example, the maple resolved the harmonic equation and got a u(t) function, but I want manipulated the data in a external programm, like gnuplot ou xmgrace.

 

Sorry my bad english!

 

wave.mw

 

How should wirte a while loop for solve nonlinear equations by newton raphson method

 


hello!

I'm new in Maple!!

I am try simulate the termal flux in composite material using heat equation and perfect contact between the materials. But I can't enter the fourier condiction and my code don't work!!

Any help??

 

> restart; with(plots); with(PDEtools); with(plottool
> eq1 := diff(u1(x, t), x, x) = k1*(diff(u1(x, t), t));
                    d  / d          \      / d          \
                   --- |--- u1(x, t)| = k1 |--- u1(x, t)|
                    dx \ dx         /      \ dt         /
> eq2 := diff(u2(x, t), x, x) = k1*(diff(u2(x, t), t));
                    d  / d          \      / d          \
                   --- |--- u2(x, t)| = k1 |--- u2(x, t)|
                    dx \ dx         /      \ dt         /
> L := 10; v1 := 20; v2 := 10; k1 = 10; k2 := 20;
                                     10
                                     20
                                     10
                                   k1 = 10
                                     20
> bc1 := u1(0, t) = v1, u1(x, 0) = 0;
                         u1(0, t) = 20, u1(x, 0) = 0
> bc2 := u2(0, t) = v2, u2(x, 0) = 0;
                         u2(0, t) = 10, u2(x, 0) = 0
> sol1 := pdsolve({bc1, eq1});
Warning: System is inconsistent

 

 

 

How should linearization a nonlinear equation with maple?

Hello

Im solving a problem. When i use solve command maple dont give me whole of amswers it just give solve the obvious problem that is zero. what i should do to it give all of the answers not just zero?

Hi

i want solve under equations but maple cannot. what i should do? please help

Hello

 Every time im working with maple and answer is in term of sin or cos maple dont calculate them for example it give me sin(pi/2) but i want it himself know that sin(pi/2)=1 some times i use of [eval] but it again dont calculate it what i should do?

 

While using the RKF45 in MAPLE to solve ODE w.r.t. time, analysis results came out without any information regarding a total number of iterations or a total number of time steps used in the actual analysis.

 

I would like to know how can this information be checked in the MAPLE.

 

Thank you very much.

 

> solve({lambda[2]*mu[2]^2*(lambda[2]+mu[2])*lambda[1]/(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)+lambda[2]*mu[2]*(mu[2]^2+mu[2]*lambda[2]+lambda[2]^2)*lambda[1]/(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)+mu[2]^4*lambda[2]*lambda[1]/((lambda[1]+mu[2])*(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4))+(1/2)*(mu[2]^3*lambda[1]+mu[2]^3*lambda[2]+lambda[1]*lambda[2]*mu[2]^2+mu[2]^2*lambda[2]^2+mu[2]*lambda[2]^3+mu[2]*lambda[1]*lambda[2]^2+lambda[1]*lambda[2]^3)*lambda[2]*lambda[1]/((lambda[1]+mu[2])*(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4))+3*mu[2]^4*lambda[1]/(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)+mu[1]*mu[2]^4*lambda[1]/((4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)*(lambda[2]+mu[1]))+mu[2]^4*lambda[2]*lambda[1]/((4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)*(lambda[2]+mu[1]))+mu[2]^3*lambda[2]*lambda[1]/(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)+(1/2)*(mu[2]^3*lambda[1]+mu[2]^3*lambda[2]+lambda[1]*lambda[2]*mu[2]^2+mu[2]^2*lambda[2]^2+mu[2]*lambda[2]^3+mu[2]*lambda[1]*lambda[2]^2+lambda[1]*lambda[2]^3)*lambda[2]*lambda[1]/(4*mu[2]^5+4*mu[2]^4*lambda[1]+4*mu[2]^4*lambda[2]+4*mu[2]^3*lambda[1]*lambda[2]+3*mu[2]^3*lambda[2]^2+3*lambda[1]*lambda[2]^2*mu[2]^2+2*mu[2]^2*lambda[2]^3+2*lambda[1]*lambda[2]^3*mu[2]+mu[2]*lambda[2]^4+lambda[1]*lambda[2]^4)-3*mu[1]*mu[2]^4/(4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)+mu[1]*mu[2]^4*lambda[2]/((4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)*(lambda[2]+mu[1]))+mu[1]^2*mu[2]^4/((4*mu[2]^4+4*mu[2]^3*lambda[2]+3*mu[2]^2*lambda[2]^2+2*mu[2]*lambda[2]^3+lambda[2]^4)*(lambda[2]+mu[1])) < 0}, [lambda[1]]);
Warning, solutions may have been lost
 

1 2 3 4 5 6 7 Last Page 1 of 50