## I try to invert this Matrix and get error...

Way I get this error ?

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## how do i plot a probabilitry function in 3 variabl...

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.

## How do I plot f(x,y,z) = x^3*y*z, constrained to x...

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

## Shooting method in maple...

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"

> 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

## Unable to plot the graphs...

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);

## output file to solution of PDE...

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

## vertical lines ...

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.

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Regards,

Matt

## output to file of an ODE solution...

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.

wave.mw

## write whlie loop ...

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

## two layer thermal flux...

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...

How should linearization a nonlinear equation with maple?

## Whole of answers not just zero...

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

## simpliy calculate...

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?

## How do I know "a total number of iterations" or "a...

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.

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