## PDE_and_BC_during_2018_err...

Hello, to all,
On my computer I have installed Windows 7 Professional, Maple 2018.2.1 and
Physics:-Version();
2019, January 5, 13:32 hours, version in the MapleCloud: 276,

version installed in this computer: 276
When I try to compute some examples from your poste "PDE_and_BC_during_2018.mw", I get an error in Example 8:
Example 8: This problem represents the temperature distribution in a thin circular plate whose lateral surfaces are insulated (Articolo example 6.9.2):
pde__8 := diff(u(r, theta, t), t) = (diff(u(r, theta, t), r)+r*(diff(u(r, theta, t), r, r))+(diff(u(r, theta, t), theta, theta))/r)/(25*r);
/
|
|
|
d                    1   |/ d                \
pde__8 := --- u(r, theta, t) = ---- ||--- u(r, theta, t)|
dt                  25 r |\ dr               /
\

2                  \
d                   |
-------- u(r, theta, t)|
/  2                \          2               |
| d                 |    dtheta                |
+ r |---- u(r, theta, t)| + -----------------------|
|   2               |              r           |
\ dr                /                          /
iv__8 := D*u(1, theta, t) = 0, u(r, 0, t) = 0, u(r, Pi, t) = 0, u(r, theta, 0) = (r-(1/3)*r^3)*sin(theta);
iv__8 := D u(1, theta, t) = 0, u(r, 0, t) = 0,

/    1  3\
u(r, Pi, t) = 0, u(r, theta, 0) = |r - - r | sin(theta)
\    3   /
pdsolve([pde__8, iv__8], u(r, theta, t), HINT = boundedseries(r = ));
Error, (in dsolve) cannot determine if this expression is true or false: not 0 <= -Pi

or I get no answer as in Example 10:
Example 10: A Laplace PDE with one homogeneous and three non-homogeneous conditions:
pde__10 := diff(u(x, y), x, x)+diff(u(x, y), y, y) = 0;
/  2         \   /  2         \
| d          |   | d          |
pde__10 := |---- u(x, y)| + |---- u(x, y)| = 0
|   2        |   |   2        |
\ dx         /   \ dy         /
iv__10 := u(0, y) = 0, u(Pi, y) = sinh(Pi)*cos(y), u(x, 0) = sin(x), u(x, Pi) = -sinh(x);
iv__10 := u(0, y) = 0, u(Pi, y) = sinh(Pi) cos(y),

u(x, 0) = sin(x), u(x, Pi) = -sinh(x)
pdsolve([pde__10, iv__10]);

There are also no answer as in Examle 10 in the Examples 15, 18, 19
Can you give me a hint,  what could be wrong?
With kind regards
Wolfgang Gellien

## DifferentialGeometry x Physics...

Hello everyone!

I am trying to calculate the Killing vectors for the metric below. For such, I used the packages DifferentialGeometry and Physics. However, I found different results these packages. Could someone explain why?  killing_test1.mw

killing_test2.mw

## Maintain Sequence Iterator In Same Line...

So I was trying to create a shorthand for creating a plot of multiple arrows, with the arrow colour dependent on the magnitude of the vector.
I currently have a set of vectors, v, I want to display, and v is the largest.

I know this could be done by creating an arrow plot for each vector seperately and then by combining them using display:
`arrow1 := arrow( v, width=0.15,length=20,color=ColorTools:-Color( (norm(v)/norm(v))*[0,0,1] ) );`
```arrow2 := arrow( v, width=0.15,length=20,color=ColorTools:-Color( (norm(v)/norm(v))*[0,0,1] ) ); ... print(plots:-display([arrow1, arrow2, ...]));```

But I was wondering if it could be done in a fashion similar to this:
```arrows := arrow([seq(v[i], i=1..4)],width=0.15,length=20,color=ColorTools:-Color((norm(v[i])/norm(v))*[0,0,1])); print(arrows);```

(btw: it works fine replacing the last i with 1, which draws all arrows nearly black, or with 4, which as you guessed, draws all arrows blue...)

Help appreciated!

## Open source Maple install for ubuntu 18.04...

Look I have actually purchased the software 3 time in total throughout my life, but i have no money at this point but i have a Linux OS now and i am enjoying learning how to use that, so i was wondering if there is a standard old verson that is open source and availble for a Linux install

## How do I plot a Fourier series for each values of ...

Sum of -(2*((-1)^n-1))*sin(n*Pi*x)*exp(-Pi^2*n^2*t)/(Pi*n) from n=20??? Thank you very much

## How to create Action in Maplet with 'for - do' com...

I try to use command "for a in 1,2 do Tangent(f, x = a) end do" in my Maplet but it does not work.

Here it is:

[Button("Tangent line", Action( Evaluate(for a in 'solve(diff(func, x) = slp, x)' do 'MMLV1'='MathML[Export]('y'=Tangent(func,x=a))' end do)))], And here is all code for my Maplet

> restart:with(Maplets[Elements]):with(Student[Calculus1]):  TL2:=Maplet([ ["Input function  f(x)=", TextField['func'](20)],[Button("Display function",Action(Evaluate('MMLV'='MathML[Export](func)')))],MathMLViewer['MMLV'](), ["Input slope", TextField['slp'](10)],  [Button("Tangent line", Action( Evaluate(for a in 'solve(diff(func, x) = slp, x)' do 'MMLV1'='MathML[Export]('y'=Tangent(func,x=a))' end do)))],   MathMLViewer['MMLV1']()   ]):  Maplets[Display](TL2):
print(`output redirected...`); # input placeholder

## Error in creating array using loop...

I am trying to create an array whose elements are from another matrix. Suppose I have a matrix of n cross m dimension my array will have a dimension of 1 cross n*m. When I create  array I am getting error. The array contains only last element of matrix. The expected answer is given in attachment.

sigma.mw

## GraphTheory: True/false-statement comparing list o...

Suppose there is a list with edges (L1): [{3,5},{4,3},{4,6},{3,2},{2,6}] and a list with vertices (L2): [1,5,4].

I would like to get a true-statement when a number of L2 appears in one of the edges of L1.

I tried the following:

for i in L1 do

ME:=member(i,L2):
print(ME):

od:

This only gives false-statements. Could anyone help me?

## pdetest fails when called after another pdetest...

I found a case where pdetest fails when called after another call to pdetest. I am using Physics version 272 from the clould. Using Maple 2018.2.1 on windows 10

```restart;
u:='u';x:='x';t:='t';
pde := diff(u(x, t), t) + diff(u(x, t),x) =0;
sol:=pdsolve(pde,u(x,t));
pdetest(sol,pde);
#0  OK

#restart;
u:='u';x:='x';t:='t';
pde:=diff(u(x,t),t)+diff(u(x,t),x)=0;
bc:=u(0,t)=0;
ic:=u(x,0)=sin(x);
sol:=pdsolve([pde,ic,bc],u(x,t)) assuming x>0;
pdetest(sol,pde);

#sol := u(x, t) = -sin(-x+t)*Heaviside(-t+x)   #OK

#-Dirac(-t+x)*sin(x)*cos(t)+Dirac(-t+x)*cos(x)*sin(t)+
Dirac(-x+t)*sin(x)*cos(t)-Dirac(-x+t)*cos(x)*sin(t)   #WRONG should be 0
```

If I run the above again, but with restart call in between active, so that all is cleared, then pdetest gives 0 as expected on the second pde, with the same solution

```restart;
u:='u';x:='x';t:='t';
pde := diff(u(x, t), t) + diff(u(x, t),x) =0;
sol:=pdsolve(pde,u(x,t));
pdetest(sol,pde);
#0   #OK

restart;
u:='u';x:='x';t:='t';
pde:=diff(u(x,t),t)+diff(u(x,t),x)=0;
bc:=u(0,t)=0;
ic:=u(x,0)=sin(x);
sol:=pdsolve([pde,ic,bc],u(x,t)) assuming x>0;
pdetest(sol,pde);

#0   #OK !! ```

can any one explain why this happens?  Is this a bug? It seems like pdetest caching problem. it remembers something from the last call and this affects the result it gives for the next call.

any work around?

## What ius wrong here?...

Another GCD attempt. Why is there a parse problem? Thanks

 > > > > Error, unable to parse > ## Why is procedure unterminated?...

I do know that Maple has a gcd command but I am just experimenting

 > > > > Error, unterminated procedure > ## reordering coefficients...

In an expression I have several terms with different coefficients and permutations of them say

aS+bc + bS+cS- + cb + others etc

I want to order them the way I want, like, say

abcS+ + bcS+cS- +bc  etc

How can I do this?

Happy New Year!

## Solve ode with time and input vector from CSV file...

I solve ode for simply DC motor system:

```J:= 0.01;b:=0.1;K:= 0.01;R:=1;L:=1;
eq1:=J*diff(theta(t),t,t)+b*diff(theta(t),t)=K*i(t):
eq2:=L*diff(i(t),t)+R*i(t)=V-K*diff(theta(t),t):

ICs:= theta(0)=0, D(theta)(0) = 0, D(theta)(0) = 0, i(0) = 0:
sol:=dsolve({eq1,eq2,ICs},numeric,parameters=[V],output=listprocedure):
sol(parameters=):
ode_x1:=sol;
ode_x1:=rhs(ode_x1);
ode_x2:=sol;
ode_x2:=rhs(ode_x2);

p1:=plot([ode_x1(t),ode_x2(t)],t=0..50,gridlines=true):
plots[display](array([p1]));```

I have time wektor and input wektor V in csv file. How to change this code to simulate

ode solution ode_x1 and ode_x2 with data from file? Now I set V as

`sol(parameters=)`

and t in

`plot([ode_x1(t),ode_x2(t)],t=0..50,gridlines=true)`

Best

## evaluate a list of polynomials over a list of valu...

Hello everybody.

This is my question. I tried to evaluate a list of polynomial over a list of values. Something like this:

eval([a*x, b*x], x = [p, q, t])

to get something like this:

[[a*p, a*q, a*t], [b*p, b*q, b*t]]

I know this method: eval~(a*x,x=~[p,q,t])  though this works for one polynomial over a list of values. Not precisely, what I am looking for.

I figured out a method that worked defining functions and with ‘apply’ and ‘map’. Here an example:

m:=t->3*2^t:

n:=t->(t+4)^2:

map(apply~,[m,n],[1,2,3]);

[[6, 12, 24], [25, 72, 147]]

However, how can I get this result using the ‘eval’ function.

Thank you all in advanced for any contribution.

## float  error in plotting graph of ODE system of...

restart; _local(gamma); _local(GAMMA); _local(Pi); _local(pi); _local(I); _local(D);
I
Warning, The imaginary unit, I, has been renamed _I
b := .45; mu[t] := 1.112; delta := .181; rho := 0.2e-1; beta[k] := .123; sigma := 0.9e-1; alpha := 0.312e-1; gamma := 0.14e-2; phi := .24; xi := .134; A[h] := .576; k := 0.1e-2; beta[c] := 0.1e-1; mu[c] := 0.19e-2; eta := .557; z := .636; phi[c] := 0.57e-1;
0.45
1.112
0.181
0.02
0.123
0.09
0.0312
0.0014
0.24
0.134
0.576
0.001
0.01
0.0019
0.557
0.636
0.057
ODE1 := diff(B(T), T) = rho*b-mu[t]*B(T)-delta*B(T);
d
--- B(T) = 0.0090 - 1.293 B(T)
dT
ODE2 := diff(C(T), T) = delta*B(T)-mu[t]*C(T)+1-rho*b-beta[k]*C(T)*H(T)+sigma*C(T);
d
--- C(T) = 0.181 B(T) - 1.022 C(T) + 0.9910 - 0.123 C(T) H(T)
dT
ODE3 := diff(D(T), T) = beta[k]*C(T)*H(T)-(mu[t]+alpha+gamma)*C(T)-phi*C(T);
d
--- D(T) = 0.123 C(T) H(T) - 1.1446 C(T) - phi C(T)
dT
ODE4 := diff(E(T), T) = alpha*D(T)-xi*E(T)-mu[t]*E(T);
d
--- E(T) = 0.0312 D(T) - 1.246 E(T)
dT
ODE5 := diff(F(T), T) = phi*D(T)+xi*E(T)-mu[t]*F(T)-sigma*C(T);
d
--- F(T) = phi D(T) + 0.134 E(T) - 1.112 F(T) - 0.09 C(T)
dT
ODE6 := diff(G(T), T) = (1-k)*A[h]-beta[c]*G(T)*H(T)-mu[c]*H(T)-eta*J(T);
d
--- G(T) = 0.575424 - 0.01 G(T) H(T) - 0.0019 H(T) - 0.557 J(T)
dT
ODE7 := diff(H(T), T) = k*A[h]+beta[c]*G(T)*H(T)-mu[c]*H(T)-z*H(T);
d
--- H(T) = 0.000576 + 0.01 G(T) H(T) - 0.6379 H(T)
dT
ODE8 := diff(J(T), T) = z*H(T)-(phi[c]+eta)*J(T);
d
--- J(T) = 0.636 H(T) - 0.614 J(T)
dT
ans := dsolve({ODE1, ODE2, ODE3, ODE4, ODE5, ODE6, ODE7, ODE8, B(0) = B0, C(0) = C0, D(0) = D0, E(0) = E0, F(0) = F0, G(0) = G0, H(0) = H0, J(0) = J0}, numeric, output = listprocedure);
Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
[T = proc(T)  ...  end;, B(T) = proc(T)  ...  end;,

C(T) = proc(T)  ...  end;, D(T) = proc(T)  ...  end;,

E(T) = proc(T)  ...  end;, F(T) = proc(T)  ...  end;,

G(T) = proc(T)  ...  end;, H(T) = proc(T)  ...  end;,

J(T) = proc(T)  ...  end;]
B0 := 100; C0 := 90; D0 := 45; E0 := 38; F0 := 100; G0 := 45; H0 := 50; J0 := 20;
100
90
45
38
100
45
50
20
ans := dsolve([ODE1, ODE2, ODE3, ODE4, ODE5, ODE6, ODE7, ODE8, B(0) = B0, C(0) = C0, D(0) = D0, E(0) = E0, F(0) = F0, G(0) = G0, H(0) = H0, J(0) = J0], numeric, output = listprocedure);
Error, (in f) unable to store 'HFloat(450.486)-HFloat(90.0)*phi' when datatype=float

﻿