Maple 13 Questions and Posts

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

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
 

HI all,

 

Let all variables be integers here.

I am trying to search 3 variables , "A","B",and "C" so that f(A*x2+B*x+C) factors into two binomials.

Here, f(y) = y2+y+19.

Choose a search space of 0<A<10 and 0<B<30 and 0<C<100.  

I am having some trouble with my Maple code.

Here is how far I got - 

Maple_coefficient_search_broken.mw

Maple_coefficient_search_broken.pdf

Regards,

Matt

 

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