How to solve this PDE equation...

Dear maple users

Greetings.

I hope you are all fine.

In this code, I am solving the PDEs via pdsolve with numeric.

There is some mistake in the boundary condition and pdsolve.

Kindly help me that to get the solution for this PDE.

In this problem h(z) is piecewise

Bc:

code:JVB.mw

Note: z=0.5:

Problem with Dsolve, error "unable to evaluate the...

Hi,

I'm facing this issue when I try to use the Dsolve function in maple, it indicates me the following error :

"Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution"

Here is part of the code :

```Lagerkraft:=rhs(Eq__Sys_4_ohneZwang[1][2])=0;
2
/ d        \
Lagerkraft := cos(phi(t)) |--- phi(t)|  a__ks m__k
\ dt       /

2
/ d        \
+ cos(phi(t)) |--- phi(t)|  a__sss m__ss
\ dt       /

2
/ d        \
+ cos(phi(t)) |--- phi(t)|  l__k m__ko
\ dt       /

2
/ d        \
+ cos(phi(t)) |--- phi(t)|  l__k m__p
\ dt       /

/  2        \
| d         |
+ |---- phi(t)| sin(phi(t)) a__ks m__k
|   2       |
\ dt        /

/  2        \
| d         |
+ |---- phi(t)| sin(phi(t)) a__sss m__ss
|   2       |
\ dt        /

/  2        \
| d         |
+ |---- phi(t)| sin(phi(t)) l__k m__ko
|   2       |
\ dt        /

/  2        \                                      /
| d         |                                      |   4
+ |---- phi(t)| sin(phi(t)) l__k m__p + 5000000 A exp|- ---
|   2       |                                      \  961
\ dt        /

2\
/            /phi(t) + Pi\                \ |
|100 Pi trunc|-----------| - 25 phi(t) + 9| | u + 200000 u A = 0
\            \   4 Pi    /                / /

indets(Lagerkraft,name)
{A, Pi, a__ks, a__sss, l__k, m__k, m__ko, m__p, m__ss, t, u}

Parameterliste__5:=[
A=4071.5*10^(-6),
a__ks=-20.94481*10^(-3),
a__kos=14.063837*10^(-3),
a__sss=0,
l__k=100*10^(-3),
m__k=11.02736,
m__ko=0.7237868,
m__p=1.437419,
m__ss=15,
u=1
];
[
Parameterliste__5 := [A = 0.004071500000, a__ks = -0.02094481000,
[

1
a__kos = 0.01406383700, a__sss = 0, l__k = --, m__k = 11.02736,
10

]
m__ko = 0.7237868, m__p = 1.437419, m__ss = 15, u = 1]
]

Lagerkraft5a:=subs(Parameterliste__5, Lagerkraft);
2
/ d        \
Lagerkraft5a := -0.01484538000 cos(phi(t)) |--- phi(t)|
\ dt       /

/  2        \
| d         |
+ 814.3000000 - 0.01484538000 |---- phi(t)| sin(phi(t)) +
|   2       |
\ dt        /

/
|   4
20357.50000 exp|- ---
\  961

2\
/            /phi(t) + Pi\                \ |
|100 Pi trunc|-----------| - 25 phi(t) + 9| | = 0
\            \   4 Pi    /                / /

indets(Lagerkraft5a,name)
{Pi, t}

Lösung_Lagerkraft:=dsolve({Lagerkraft5a,AB},phi(t),numeric,dsolve_options);
```

Thanks

Bug in abs/Heaviside...

Hi folks, here's a bug in converting abs to Heavisides:

Converting the derivative of the abs function to a piecewise function is fine:
convert(abs(1,x),piecewise);
returns
piecewise(x < 0, -1, x = 0, undefined, 0 < x, 1);

Whereas,
convert(abs(1,x),Heaviside);
returns 1.

abs_problem.mw

 > restart; interface(version);
 (1)
 > convert(abs(1,x),piecewise); convert(abs(1,x),Heaviside); convert(%%,Heaviside);
 (2)
 > abs(x)=convert(abs(x),Heaviside); diff(%,x); strange:=convert(%,Heaviside); eval(subs(x=-1,%));
 (3)
 > plot([(abs(x)),lhs(strange),rhs(strange)],x=-5..5,colour=[black,red,blue]);
 >
 >

Improving time consuming code...

Hi

The following code is time consuming. Please improve the code, if it is possible. Thanks for taking your time

restart;

T := time():
M := 50:
Digits := 30:
L := 500:
R := (1/2):
nu := 0.3:
Em := 0.70e11:
N := 1:
Ec := 0.380e12:
E:= Em*(1-(y/h+1/2)^N)+Ec*(y/h+1/2)^N:
X :=(int(E*(z+(1/2)*R), [z = y-(1/2)*R .. 0, y = -(1/2)*R .. (1/2)*R]))/(int(E, [z = y-(1/2)*R .. 0, y = -(1/2)*R .. (1/2)*R])):
beta := Pi^2/L^2:
G := E/(2*(1+nu)):
phi := add(b[n]*y^n, n = 0 .. M):
Eq := diff(phi, y\$2)+(diff(E, y))*(diff(phi, y))/E+((diff(E, y\$2))/E-((diff(E, y))/E)^2)*phi-2*beta*(1+nu)*(phi-1):
st := [seq(coeftayl(Eq, y = 0, j), j = 0 .. M-2)]:
for k to M-1 do
b[k+1] := solve(st[k], b[k+1])
end do:
phi := subs(y = y-X, phi):
phi := subs(solve({eval(phi, y = -(1/2)*R+X), subs(y = f, phi)}, {b[0], b[1]}), phi):
f := piecewise(`and`(z >= -R, z <= 0), z+(1/2)*R+X, -z+(1/2)*R+X):
Digits := 4:
int(phi*G, [z = y-(1/2)*R .. 0, y = -(1/2)*R .. (1/2)*R], numeric)+int(phi*G, [z = 0 .. -y+(1/2)*R, y = -(1/2)*R .. (1/2)*R], numeric);

Time = Time()-T;

Note that the calculation of the integration requires alot of time. Both returns a similar result (calculation of an integration is sufficient)

launch a maple code from a texteditor (such as not...

Hello,

I'm trying to use a text editor (notepad++) to developp a code in Maple.

Before creating a package, i would like to test step by step the different procedures that i create.

To do so, i would like to launch some procedures created in notepad++. I guess i have to call the maple kernel from notepad++. How can i do to call the maple kernel from a editor (in my case notepad++) ?

Next, would it be possible for me to test directly on a worksheet a procedure that i have been created in notepad and launched from notepad ?

Animation optimization (phase portrait)...

hi! lately I'm thinking about animating complex phase portraits so I tried something like this:

restart;
with(plots);
f := (a, z) -> (z*a - 1)/(z^2 + z + 1);
display(seq(densityplot(proc(x, y) local res; res := evalhf(argument(f(1/100*a, y + x*I))); return res; end proc, -4 .. 4, -4 .. 4, axes = boxed, view = [-2 .. 2, -2 .. 2], restricttoranges, colorstyle = HUE, style = surface, grid = [201, 201]), a = 1 .. 200), insequence = true);

but this takes a long time to load. Do you how can we optimizate this code?

symbol dollar in argument in a procedure...

Hello,

In a maple code, i have the symbol dollar as an the last argument of a procedure.

What is the meaning of the use of dollar symbol as an argument in a maple procedure ?

Bug in Maple 2021?...

Hi,

I just upgraded to Maple 2021 and started getting strange results - similar calculations seemed to work in Maple 2020.

I am looking at correlated bivariate normal distributions. When doing a fully symbolic verification of the normalization, I get an incorrect result of infinity. I also get strange results when integrating over a circular region, but the normalization seemed to be a very elementary calculation.

Maybe someone can check this make sure I'm not losing my marbles. I've attached a worksheet.

Thanks.

Bivariate_Gaussian.mw

Three rolling circles...

hi, do you know how can we plot analogy situation from this post:

https://mathematica.stackexchange.com/questions/100051/dynamic-epicycles/100108#100108

I really like simplicity and beauty of the idea from:

https://www.mapleprimes.com/posts/206167-Procedures-For-Two-Animations

and I wonder if it would be possible to add a third rolling circle similarly not including such long code from first page.

animation and range problem error...

Is there a reason that an angle theta from zero to pi/2 (0 to 90 deg) returns as invalid for an animation range?  I am trying to rotate a vector 2D for visualization.  This is build-up towards a 3d rotating vector in an animation.

Here is the code: theta is the arrow tip rotation's location via cos(theta), sin(theta) coordinates in a 2D vector.

animate(arrow, [<cos(theta), sin(theta)>, width = [0.05, relative], view = [-1 .. 2, -1 .. 2], color = "blue"], theta = 0 .. Pi/2)

ErrorMessage:

Error, (in plots/animate) 0 = 0 .. (1/2)*Pi  is an invalid animation range

Bill

Maple PDE solver...

Hello,

does Maple have a PDE solver? I want to solve the following inhomogeneous case of the heat equation:

diff(u(t,x,y,z),t)=k*Laplacian(u(t,x,y,z))+l*u(t,x,y,z)+m

with boundary conditions u(t,0,y,z)=u(t,L,y,z)=u(t,x,0,z)=u(t,x,L,z)=u(t,x,y,0)=u(t,x,y,L)=0. The initial condition is not fixed, as I want to try different cases. It will probably be some sinusoidal spatial function. I would prefer an analytic solution but I could live with a numerical one. If not in three spatial dimensions then even a solution with one dimension would be useful. I would appreciate any help.

Thank you.

sort an expression with order of a symbol...

How can this expression sorted in order of the symbol "y"? I want the terms with y locate at the beginnig.

 > restart:
 > f:=x^2+x^y+1-z
 (1)
 >

How do i solve a diff problem with arctan. when ar...

As the title, who can help me fix the problem like this

theta:= diff(arctan(y,x)):

W:= piecewise(

theta>-Pi/2 and theta< -Pi/2+10, 1+A+B*cos(theta),

theta>-Pi/2+10 and theta< Pi/2-10. 1-A+B*cos(thea));

there always plotout the undefined when acrtan(y,x)=Pi/2,

How can I ignore this undefined or define another value for W when acrtan(y,x)=Pi/2

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