how do I integrate HeunB function with complex arg...

I am trying to calculate the following integra
r*rr*g1^2*h1^2*f1^2*fh1^2*exp(-2*t)/t

here g1 is a kummerM functin in s, and also h1 is another kummerM function  in ss, and f1 and fh1 are the HeunB functions with complex arguments in r and rr. and t=sqrt((r-rr)^2+(s-ss)^2).I would like to integte over dr drr ds dss

Why Minus an Integras Sign Places parentheses Arou...

I am using an integal sign using Int. If there is a minus sign in front of it, then

I get the expression -(Int ... dx). Why is the parenthesis there? Can we avoind it?

Thank you!

mapleatha

Why Does Maple Give Me the Answer Like This?...

Why does Maple give me an answer like this?

How do I force Maple to automatically multiply the exponents in the denominator and eliminate the factor y^2?

Simplify will not do it.

Thank you!

mapleatha

Getting Rid of _F1, _F2, Etc., in the Solution of...

I am solving a PDE whose solution is the integrating factor MU of a given 1st order ODE. I get

I only need one of these solutions. How do I get rid of _F1? Can I make it to be the identity function? That is exactly what I need.

Thank you, as always!

mapleatha

Why Doesn't Maple Solve This System?...

I cannot get the answer (m=2,n=2) to the following problem on two equations from Maple 13.

(13/4)*m-(7/4)*n-3 = 0,
-(17/2)*n*2^n +34*m= 0

I get:

{m = (7/13)*RootOf(13*_Z*2^_Z-28*_Z-48)+12/13, n = RootOf(13*_Z*2^_Z-28*_Z-48)}

Thank you very much.

mapleatha

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

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